logo-type-white

Ohm’s Law Practice Problems | Review and Examples

  • The Albert Team
  • Last Updated On: December 5, 2023

problem solving electrical circuit

Welcome to the fascinating world of electrical principles, where understanding Ohm’s Law is not just a skill but a necessity. Often considered the backbone of electrical engineering and physics, Ohm’s Law is a fundamental concept that illuminates the relationship between voltage, current, and resistance in an electrical circuit. In this comprehensive guide, we will cover the core of Ohm’s Law, explore its fundamental formula, and work through a series of Ohm’s Law practice problems. Mastering Ohm’s Law is a step towards unraveling the complexities of electronics.

What Does Ohm’s Law State?

Ohm’s Law is a fundamental principle in electronics and physics, providing a simple yet powerful way to understand the relationship between voltage, current, and resistance in electrical circuits. At its core, Ohm’s Law states that the current through a conductor between two points is directly proportional to the voltage across these points and inversely proportional to the resistance between them. This relationship is elegantly captured in the formula V = IR , where V stands for voltage, I for current, and R for resistance.

Understanding Voltage, Current, and Resistance

In order to fully appreciate Ohm’s law, let’s review the three components.

  • Voltage (V) : Often described as the electrical force or pressure that drives the flow of electrons through a conductor. It’s the potential difference between two points in a circuit.
  • Current (I) : This is the flow of electrical charge, measured in amperes (A). It represents how many electrons are flowing through the circuit.
  • Resistance (R) : Resistance is the opposition to the current flow in a circuit. It’s measured in ohms (Ω) and depends on the material, size, and temperature of the conductor.

By manipulating the Ohm’s Law formula, you can solve for any one of these three variables if the other two are known. This makes it an invaluable tool for understanding and designing electrical circuits.

Practical Applications

Ohm’s Law isn’t just a theoretical concept; it has numerous practical applications in everyday life and various industries. Here are a few examples:

  • Electronics Design: Engineers use Ohm’s Law to design circuits, select appropriate components, and ensure electrical devices function safely and efficiently.
  • Troubleshooting Electrical Problems: Technicians often use Ohm’s Law to diagnose issues in electrical systems, such as finding short circuits or identifying components that are not functioning correctly.
  • Educational Purposes: Ohm’s Law is a fundamental concept taught in physics and electronics courses, helping students understand the basics of electrical circuits.
  • Power Management: In larger-scale applications like power distribution, Ohm’s Law helps calculate the load that can be safely put on electrical systems without causing damage or inefficiency.

problem solving electrical circuit

Understanding Ohm’s Law opens up possibilities for creating, managing, and troubleshooting electrical systems, from the smallest electronic devices to large-scale power grids.

What is the Formula for Ohm’s Law?

Ohm’s Law is elegant in its formulation, providing a precise mathematical relationship between voltage, current, and resistance in an electrical circuit.


V = IR

In the formula for Ohm’s Law, V represents voltage measured in volts (V), I is the current measured in amperes (A), and R is the resistance measured in ohms (Ω). This formula is the cornerstone for analyzing and understanding electrical circuits, requiring two variables to solve.

Ohm’s Law Triangle

The Ohm’s Law triangle is a helpful tool for remembering how to calculate voltage, current, and resistance. It visually represents the formula V=IR in a graphic format, with V at the top, I on the left, and R on the right. By covering the variable you want to calculate, the other two variables show how they relate. For example, covering V shows I\times R , covering I shows /frac{V}{R} , and covering R shows \frac{V}{I} . This tool is handy for beginners and a reference for quick calculations.

The Ohm's Law Triangle is a useful tool for solving Ohm's Law practice problems.

Strategies for Solving Ohm’s Law Practice Problems

When solving problems using Ohm’s Law, it’s important to follow a systematic approach:

  • Identify Known Quantities: Start by determining which of the three variables (voltage, current, resistance) are known.
  • Determine the Unknown: Figure out which variable you need to calculate.
  • Use the Ohm’s Law Circle: Utilize the Ohm’s Law circle to understand the relationship between the variables and to choose the correct formula.
  • Solve Step-by-Step: Apply the formula and solve for the unknown variable step-by-step, ensuring accuracy in your calculations.
  • Check Units: Always check that your units are consistent (volts for voltage, amperes for current, ohms for resistance) and convert if necessary.

By applying these strategies, you can effectively use Ohm’s Law to solve a wide range of electrical problems, enhancing your understanding and skills in electrical theory and practice.

Examples of Ohm’s Law

Calculating Current: If a light bulb has a resistance of 240\text{ ohms} and is connected to a 120\text{-volt} power source, the current flowing through it can be calculated as:

Determining Voltage: For a toaster that draws a current of 5\text{ amperes} and has a resistance of 10\text{ ohms} , the voltage across it is:

Finding Resistance: If a hairdryer operates at 220\text{ volts} and draws a current of 11\text{ amperes} , its resistance is:

These examples demonstrate how Ohm’s Law is applied in practical situations, providing a clear understanding of how electrical components function in various devices.

Ohm’s Law Practice Problems

Here are eight practice problems involving Ohm’s Law, arranged in order of increasing complexity. These problems will help you apply the concepts of voltage, current, and resistance in various scenarios. Work through these on your own, then scroll down for solutions.

1. Basic Current Calculation

A circuit with a 9\text{-volt} battery and a resistor of 3\text{ ohms} . What is the current flowing through the circuit?

2. Resistance Determination

Find the resistance of a bulb that draws 0.5\text{ amperes} from a 120\text{-volt} supply.

3. Voltage Calculation

What is the voltage across a resistor of 15\text{ ohms} through which a current of 2\text{ amperes} is flowing?

4. Multiple Resistors (Series) 

In a series circuit with a 12\text{-volt} battery, if there are two resistors of 4\text{ ohms} and 6\text{ ohms} , what is the current flowing through the circuit?

5. Multiple Resistors (Parallel)

Calculate the total resistance in a parallel circuit with two resistors of 5\text{ ohms} and 10\text{ ohms} . If a voltage of 12\text{-volts} is applied across the circuit, what is the total current flowing through the circuit?

6. Combined Ohm’s Law and Power

A device using 18\text{ watts} of power is connected to a 9\text{-volt} battery. Calculate the current drawn by the device and determine the resistance of the device.

7. Variable Resistance

If the current in a circuit is 0.25\text{ amperes} and the voltage is 10\text{ volts} , what must be the resistance?

8. Complex Circuit Analysis

In a circuit, a 6\text{-ohm} resistor and a 12\text{-ohm} resistor are connected in series to a 9\text{-volt} battery. Calculate the current through each resistor.

problem solving electrical circuit

Solutions to Ohm’s Law Practice Problems

Are you ready to see how you did? Review below to see the solutions for the Ohm’s Law practice problems.

We have a simple circuit with a 9\text{ V} battery and a 3\ \Omega resistor. In order to solve this, use Ohm’s Law, V=IR to find the current:

Therefore, the current flowing through this circuit is 3\text{ amperes} , typical for small electronic devices.

A bulb is connected to a 120\text{ V} supply and draws 0.5\text{ A} .To find the resistance, rearrange Ohm’s Law to R = V/I :

The bulb has a resistance of 240\ \Omega , indicating it’s suitable for moderate power applications.

A resistor of 15\ \Omega carries a current of 2\text{ A} . Apply V=IR to find the voltage across the resistor:

The voltage across this resistor is 30\text{ V} , typical for small household circuits.

We have a series circuit with a 12\text{ V} battery and two resistors ( 4\ \Omega and 6\ \Omega ). First, sum the resistances in series. Then, apply Ohm’s Law.

Summing the resistance:

Now, apply Ohm’s Law with the total resistance, rearranged for the current:

The current of 1.2\text{ A} flows uniformly through each component in this series circuit.

In this scenario, there is a parallel circuit with two resistors of 5\ \Omega and 10\ \Omega . First, calculate the total resistance in parallel using the reciprocal formula:

Then, apply Ohm’s Law with the total resistance, rearranged for the current:

The total current flowing through the circuit is approximately 3.6\text{ A} .

An 18\text{ W} device is connected to a 9\text{ V} battery. First, find the current using by rearranging the power formula P=VI :

The device draws a current of 2\text{ A} . Next, use Ohm’s Law rearranged for resistance:

The device’s resistance is 4.5\ \Omega .

For a circuit with a current of 0.25\text{ A} and a voltage of 10\text{ V} , apply Ohm’s Law to find the resistance:

The circuit has a resistance of 40\ \Omega , indicating a relatively high resistance for the given current and voltage.

First, calculate the total resistance:

For a series circuit, all elements receive the same current. Each resistor in this series circuit experiences a current of 0.5\text{ A} .

As we reach the end of our exploration into Ohm’s Law, it’s clear that this fundamental principle is more than just a formula; it’s a key to unlocking the mysteries of electrical circuits. Through this guide, we’ve journeyed from the basic understanding of voltage, current, and resistance to applying these concepts in various practical scenarios. The practice problems provided various challenges, from straightforward calculations to more complex circuit analyses, each designed to strengthen your grasp of Ohm’s Law.

Remember, the journey of mastering Ohm’s Law is as much about practice as it is about understanding the theory. Each problem you solve, and each circuit you analyze adds to your skill set, making you more adept at navigating the world of electronics.

Interested in a school license?​

Popular posts.

AP® Physics I score calculator

AP® Score Calculators

Simulate how different MCQ and FRQ scores translate into AP® scores

problem solving electrical circuit

AP® Review Guides

The ultimate review guides for AP® subjects to help you plan and structure your prep.

problem solving electrical circuit

Core Subject Review Guides

Review the most important topics in Physics and Algebra 1 .

problem solving electrical circuit

SAT® Score Calculator

See how scores on each section impacts your overall SAT® score

problem solving electrical circuit

ACT® Score Calculator

See how scores on each section impacts your overall ACT® score

problem solving electrical circuit

Grammar Review Hub

Comprehensive review of grammar skills

problem solving electrical circuit

AP® Posters

Download updated posters summarizing the main topics and structure for each AP® exam.

Youtube

  • TPC and eLearning
  • What's NEW at TPC?
  • Read Watch Interact
  • Practice Review Test
  • Teacher-Tools
  • Subscription Selection
  • Seat Calculator
  • Ad Free Account
  • Edit Profile Settings
  • Classes (Version 2)
  • Student Progress Edit
  • Task Properties
  • Export Student Progress
  • Task, Activities, and Scores
  • Metric Conversions Questions
  • Metric System Questions
  • Metric Estimation Questions
  • Significant Digits Questions
  • Proportional Reasoning
  • Acceleration
  • Distance-Displacement
  • Dots and Graphs
  • Graph That Motion
  • Match That Graph
  • Name That Motion
  • Motion Diagrams
  • Pos'n Time Graphs Numerical
  • Pos'n Time Graphs Conceptual
  • Up And Down - Questions
  • Balanced vs. Unbalanced Forces
  • Change of State
  • Force and Motion
  • Mass and Weight
  • Match That Free-Body Diagram
  • Net Force (and Acceleration) Ranking Tasks
  • Newton's Second Law
  • Normal Force Card Sort
  • Recognizing Forces
  • Air Resistance and Skydiving
  • Solve It! with Newton's Second Law
  • Which One Doesn't Belong?
  • Component Addition Questions
  • Head-to-Tail Vector Addition
  • Projectile Mathematics
  • Trajectory - Angle Launched Projectiles
  • Trajectory - Horizontally Launched Projectiles
  • Vector Addition
  • Vector Direction
  • Which One Doesn't Belong? Projectile Motion
  • Forces in 2-Dimensions
  • Being Impulsive About Momentum
  • Explosions - Law Breakers
  • Hit and Stick Collisions - Law Breakers
  • Case Studies: Impulse and Force
  • Impulse-Momentum Change Table
  • Keeping Track of Momentum - Hit and Stick
  • Keeping Track of Momentum - Hit and Bounce
  • What's Up (and Down) with KE and PE?
  • Energy Conservation Questions
  • Energy Dissipation Questions
  • Energy Ranking Tasks
  • LOL Charts (a.k.a., Energy Bar Charts)
  • Match That Bar Chart
  • Words and Charts Questions
  • Name That Energy
  • Stepping Up with PE and KE Questions
  • Case Studies - Circular Motion
  • Circular Logic
  • Forces and Free-Body Diagrams in Circular Motion
  • Gravitational Field Strength
  • Universal Gravitation
  • Angular Position and Displacement
  • Linear and Angular Velocity
  • Angular Acceleration
  • Rotational Inertia
  • Balanced vs. Unbalanced Torques
  • Getting a Handle on Torque
  • Torque-ing About Rotation
  • Properties of Matter
  • Fluid Pressure
  • Buoyant Force
  • Sinking, Floating, and Hanging
  • Pascal's Principle
  • Flow Velocity
  • Bernoulli's Principle
  • Balloon Interactions
  • Charge and Charging
  • Charge Interactions
  • Charging by Induction
  • Conductors and Insulators
  • Coulombs Law
  • Electric Field
  • Electric Field Intensity
  • Polarization
  • Case Studies: Electric Power
  • Know Your Potential
  • Light Bulb Anatomy
  • I = ∆V/R Equations as a Guide to Thinking
  • Parallel Circuits - ∆V = I•R Calculations
  • Resistance Ranking Tasks
  • Series Circuits - ∆V = I•R Calculations
  • Series vs. Parallel Circuits

Equivalent Resistance

  • Period and Frequency of a Pendulum
  • Pendulum Motion: Velocity and Force
  • Energy of a Pendulum
  • Period and Frequency of a Mass on a Spring
  • Horizontal Springs: Velocity and Force
  • Vertical Springs: Velocity and Force
  • Energy of a Mass on a Spring
  • Decibel Scale
  • Frequency and Period
  • Closed-End Air Columns
  • Name That Harmonic: Strings
  • Rocking the Boat
  • Wave Basics
  • Matching Pairs: Wave Characteristics
  • Wave Interference
  • Waves - Case Studies
  • Color Addition and Subtraction
  • Color Filters
  • If This, Then That: Color Subtraction
  • Light Intensity
  • Color Pigments
  • Converging Lenses
  • Curved Mirror Images
  • Law of Reflection
  • Refraction and Lenses
  • Total Internal Reflection
  • Who Can See Who?
  • Formulas and Atom Counting
  • Atomic Models
  • Bond Polarity
  • Entropy Questions
  • Cell Voltage Questions
  • Heat of Formation Questions
  • Reduction Potential Questions
  • Oxidation States Questions
  • Measuring the Quantity of Heat
  • Hess's Law
  • Oxidation-Reduction Questions
  • Galvanic Cells Questions
  • Thermal Stoichiometry
  • Molecular Polarity
  • Quantum Mechanics
  • Balancing Chemical Equations
  • Bronsted-Lowry Model of Acids and Bases
  • Classification of Matter
  • Collision Model of Reaction Rates
  • Density Ranking Tasks
  • Dissociation Reactions
  • Complete Electron Configurations
  • Elemental Measures
  • Enthalpy Change Questions
  • Equilibrium Concept
  • Equilibrium Constant Expression
  • Equilibrium Calculations - Questions
  • Equilibrium ICE Table
  • Intermolecular Forces Questions
  • Ionic Bonding
  • Lewis Electron Dot Structures
  • Limiting Reactants
  • Line Spectra Questions
  • Mass Stoichiometry
  • Measurement and Numbers
  • Metals, Nonmetals, and Metalloids
  • Metric Estimations
  • Metric System
  • Molarity Ranking Tasks
  • Mole Conversions
  • Name That Element
  • Names to Formulas
  • Names to Formulas 2
  • Nuclear Decay
  • Particles, Words, and Formulas
  • Periodic Trends
  • Precipitation Reactions and Net Ionic Equations
  • Pressure Concepts
  • Pressure-Temperature Gas Law
  • Pressure-Volume Gas Law
  • Chemical Reaction Types
  • Significant Digits and Measurement
  • States Of Matter Exercise
  • Stoichiometry Law Breakers
  • Stoichiometry - Math Relationships
  • Subatomic Particles
  • Spontaneity and Driving Forces
  • Gibbs Free Energy
  • Volume-Temperature Gas Law
  • Acid-Base Properties
  • Energy and Chemical Reactions
  • Chemical and Physical Properties
  • Valence Shell Electron Pair Repulsion Theory
  • Writing Balanced Chemical Equations
  • Mission CG1
  • Mission CG10
  • Mission CG2
  • Mission CG3
  • Mission CG4
  • Mission CG5
  • Mission CG6
  • Mission CG7
  • Mission CG8
  • Mission CG9
  • Mission EC1
  • Mission EC10
  • Mission EC11
  • Mission EC12
  • Mission EC2
  • Mission EC3
  • Mission EC4
  • Mission EC5
  • Mission EC6
  • Mission EC7
  • Mission EC8
  • Mission EC9
  • Mission RL1
  • Mission RL2
  • Mission RL3
  • Mission RL4
  • Mission RL5
  • Mission RL6
  • Mission KG7
  • Mission RL8
  • Mission KG9
  • Mission RL10
  • Mission RL11
  • Mission RM1
  • Mission RM2
  • Mission RM3
  • Mission RM4
  • Mission RM5
  • Mission RM6
  • Mission RM8
  • Mission RM10
  • Mission LC1
  • Mission RM11
  • Mission LC2
  • Mission LC3
  • Mission LC4
  • Mission LC5
  • Mission LC6
  • Mission LC8
  • Mission SM1
  • Mission SM2
  • Mission SM3
  • Mission SM4
  • Mission SM5
  • Mission SM6
  • Mission SM8
  • Mission SM10
  • Mission KG10
  • Mission SM11
  • Mission KG2
  • Mission KG3
  • Mission KG4
  • Mission KG5
  • Mission KG6
  • Mission KG8
  • Mission KG11
  • Mission F2D1
  • Mission F2D2
  • Mission F2D3
  • Mission F2D4
  • Mission F2D5
  • Mission F2D6
  • Mission KC1
  • Mission KC2
  • Mission KC3
  • Mission KC4
  • Mission KC5
  • Mission KC6
  • Mission KC7
  • Mission KC8
  • Mission AAA
  • Mission SM9
  • Mission LC7
  • Mission LC9
  • Mission NL1
  • Mission NL2
  • Mission NL3
  • Mission NL4
  • Mission NL5
  • Mission NL6
  • Mission NL7
  • Mission NL8
  • Mission NL9
  • Mission NL10
  • Mission NL11
  • Mission NL12
  • Mission MC1
  • Mission MC10
  • Mission MC2
  • Mission MC3
  • Mission MC4
  • Mission MC5
  • Mission MC6
  • Mission MC7
  • Mission MC8
  • Mission MC9
  • Mission RM7
  • Mission RM9
  • Mission RL7
  • Mission RL9
  • Mission SM7
  • Mission SE1
  • Mission SE10
  • Mission SE11
  • Mission SE12
  • Mission SE2
  • Mission SE3
  • Mission SE4
  • Mission SE5
  • Mission SE6
  • Mission SE7
  • Mission SE8
  • Mission SE9
  • Mission VP1
  • Mission VP10
  • Mission VP2
  • Mission VP3
  • Mission VP4
  • Mission VP5
  • Mission VP6
  • Mission VP7
  • Mission VP8
  • Mission VP9
  • Mission WM1
  • Mission WM2
  • Mission WM3
  • Mission WM4
  • Mission WM5
  • Mission WM6
  • Mission WM7
  • Mission WM8
  • Mission WE1
  • Mission WE10
  • Mission WE2
  • Mission WE3
  • Mission WE4
  • Mission WE5
  • Mission WE6
  • Mission WE7
  • Mission WE8
  • Mission WE9
  • Vector Walk Interactive
  • Name That Motion Interactive
  • Kinematic Graphing 1 Concept Checker
  • Kinematic Graphing 2 Concept Checker
  • Graph That Motion Interactive
  • Two Stage Rocket Interactive
  • Rocket Sled Concept Checker
  • Force Concept Checker
  • Free-Body Diagrams Concept Checker
  • Free-Body Diagrams The Sequel Concept Checker
  • Skydiving Concept Checker
  • Elevator Ride Concept Checker
  • Vector Addition Concept Checker
  • Vector Walk in Two Dimensions Interactive
  • Name That Vector Interactive
  • River Boat Simulator Concept Checker
  • Projectile Simulator 2 Concept Checker
  • Projectile Simulator 3 Concept Checker
  • Hit the Target Interactive
  • Turd the Target 1 Interactive
  • Turd the Target 2 Interactive
  • Balance It Interactive
  • Go For The Gold Interactive
  • Egg Drop Concept Checker
  • Fish Catch Concept Checker
  • Exploding Carts Concept Checker
  • Collision Carts - Inelastic Collisions Concept Checker
  • Its All Uphill Concept Checker
  • Stopping Distance Concept Checker
  • Chart That Motion Interactive
  • Roller Coaster Model Concept Checker
  • Uniform Circular Motion Concept Checker
  • Horizontal Circle Simulation Concept Checker
  • Vertical Circle Simulation Concept Checker
  • Race Track Concept Checker
  • Gravitational Fields Concept Checker
  • Orbital Motion Concept Checker
  • Angular Acceleration Concept Checker
  • Balance Beam Concept Checker
  • Torque Balancer Concept Checker
  • Aluminum Can Polarization Concept Checker
  • Charging Concept Checker
  • Name That Charge Simulation
  • Coulomb's Law Concept Checker
  • Electric Field Lines Concept Checker
  • Put the Charge in the Goal Concept Checker
  • Circuit Builder Concept Checker (Series Circuits)
  • Circuit Builder Concept Checker (Parallel Circuits)
  • Circuit Builder Concept Checker (∆V-I-R)
  • Circuit Builder Concept Checker (Voltage Drop)
  • Equivalent Resistance Interactive
  • Pendulum Motion Simulation Concept Checker
  • Mass on a Spring Simulation Concept Checker
  • Particle Wave Simulation Concept Checker
  • Boundary Behavior Simulation Concept Checker
  • Slinky Wave Simulator Concept Checker
  • Simple Wave Simulator Concept Checker
  • Wave Addition Simulation Concept Checker
  • Standing Wave Maker Simulation Concept Checker
  • Color Addition Concept Checker
  • Painting With CMY Concept Checker
  • Stage Lighting Concept Checker
  • Filtering Away Concept Checker
  • InterferencePatterns Concept Checker
  • Young's Experiment Interactive
  • Plane Mirror Images Interactive
  • Who Can See Who Concept Checker
  • Optics Bench (Mirrors) Concept Checker
  • Name That Image (Mirrors) Interactive
  • Refraction Concept Checker
  • Total Internal Reflection Concept Checker
  • Optics Bench (Lenses) Concept Checker
  • Kinematics Preview
  • Velocity Time Graphs Preview
  • Moving Cart on an Inclined Plane Preview
  • Stopping Distance Preview
  • Cart, Bricks, and Bands Preview
  • Fan Cart Study Preview
  • Friction Preview
  • Coffee Filter Lab Preview
  • Friction, Speed, and Stopping Distance Preview
  • Up and Down Preview
  • Projectile Range Preview
  • Ballistics Preview
  • Juggling Preview
  • Marshmallow Launcher Preview
  • Air Bag Safety Preview
  • Colliding Carts Preview
  • Collisions Preview
  • Engineering Safer Helmets Preview
  • Push the Plow Preview
  • Its All Uphill Preview
  • Energy on an Incline Preview
  • Modeling Roller Coasters Preview
  • Hot Wheels Stopping Distance Preview
  • Ball Bat Collision Preview
  • Energy in Fields Preview
  • Weightlessness Training Preview
  • Roller Coaster Loops Preview
  • Universal Gravitation Preview
  • Keplers Laws Preview
  • Kepler's Third Law Preview
  • Charge Interactions Preview
  • Sticky Tape Experiments Preview
  • Wire Gauge Preview
  • Voltage, Current, and Resistance Preview
  • Light Bulb Resistance Preview
  • Series and Parallel Circuits Preview
  • Thermal Equilibrium Preview
  • Linear Expansion Preview
  • Heating Curves Preview
  • Electricity and Magnetism - Part 1 Preview
  • Electricity and Magnetism - Part 2 Preview
  • Vibrating Mass on a Spring Preview
  • Period of a Pendulum Preview
  • Wave Speed Preview
  • Slinky-Experiments Preview
  • Standing Waves in a Rope Preview
  • Sound as a Pressure Wave Preview
  • DeciBel Scale Preview
  • DeciBels, Phons, and Sones Preview
  • Sound of Music Preview
  • Shedding Light on Light Bulbs Preview
  • Models of Light Preview
  • Electromagnetic Radiation Preview
  • Electromagnetic Spectrum Preview
  • EM Wave Communication Preview
  • Digitized Data Preview
  • Light Intensity Preview
  • Concave Mirrors Preview
  • Object Image Relations Preview
  • Snells Law Preview
  • Reflection vs. Transmission Preview
  • Magnification Lab Preview
  • Reactivity Preview
  • Ions and the Periodic Table Preview
  • Periodic Trends Preview
  • Chemical Reactions Preview
  • Intermolecular Forces Preview
  • Melting Points and Boiling Points Preview
  • Bond Energy and Reactions Preview
  • Reaction Rates Preview
  • Ammonia Factory Preview
  • Stoichiometry Preview
  • Nuclear Chemistry Preview
  • Gaining Teacher Access
  • Algebra Based Physics Course
  • Tasks and Classes
  • Tasks - Classic
  • Subscription
  • Subscription Locator
  • 1-D Kinematics
  • Newton's Laws
  • Vectors - Motion and Forces in Two Dimensions
  • Momentum and Its Conservation
  • Work and Energy
  • Circular Motion and Satellite Motion
  • Thermal Physics
  • Static Electricity
  • Electric Circuits
  • Vibrations and Waves
  • Sound Waves and Music
  • Light and Color
  • Reflection and Mirrors
  • About the Physics Interactives
  • Task Tracker
  • Usage Policy
  • Newtons Laws
  • Vectors and Projectiles
  • Forces in 2D
  • Momentum and Collisions
  • Circular and Satellite Motion
  • Balance and Rotation
  • Electromagnetism
  • Waves and Sound
  • Atomic Physics
  • Forces in Two Dimensions
  • Work, Energy, and Power
  • Circular Motion and Gravitation
  • Sound Waves
  • 1-Dimensional Kinematics
  • Circular, Satellite, and Rotational Motion
  • Einstein's Theory of Special Relativity
  • Waves, Sound and Light
  • QuickTime Movies
  • About the Concept Builders
  • Pricing For Schools
  • Directions for Version 2
  • Measurement and Units
  • Relationships and Graphs
  • Rotation and Balance
  • Vibrational Motion
  • Reflection and Refraction
  • Teacher Accounts
  • Task Tracker Directions
  • Kinematic Concepts
  • Kinematic Graphing
  • Wave Motion
  • Sound and Music
  • About CalcPad
  • 1D Kinematics
  • Vectors and Forces in 2D
  • Simple Harmonic Motion
  • Rotational Kinematics
  • Rotation and Torque
  • Rotational Dynamics
  • Electric Fields, Potential, and Capacitance
  • Transient RC Circuits
  • Light Waves
  • Units and Measurement
  • Stoichiometry
  • Molarity and Solutions
  • Thermal Chemistry
  • Acids and Bases
  • Kinetics and Equilibrium
  • Solution Equilibria
  • Oxidation-Reduction
  • Nuclear Chemistry
  • Newton's Laws of Motion
  • Work and Energy Packet
  • Static Electricity Review
  • NGSS Alignments
  • 1D-Kinematics
  • Projectiles
  • Circular Motion
  • Magnetism and Electromagnetism
  • Graphing Practice
  • About the ACT
  • ACT Preparation
  • For Teachers
  • Other Resources
  • Solutions Guide
  • Solutions Guide Digital Download
  • Motion in One Dimension
  • Work, Energy and Power
  • Algebra Based Physics
  • Honors Physics
  • Conceptual Physics
  • Other Tools
  • Frequently Asked Questions
  • Purchasing the Download
  • Purchasing the CD
  • Purchasing the Digital Download
  • About the NGSS Corner
  • NGSS Search
  • Force and Motion DCIs - High School
  • Energy DCIs - High School
  • Wave Applications DCIs - High School
  • Force and Motion PEs - High School
  • Energy PEs - High School
  • Wave Applications PEs - High School
  • Crosscutting Concepts
  • The Practices
  • Physics Topics
  • NGSS Corner: Activity List
  • NGSS Corner: Infographics
  • About the Toolkits
  • Position-Velocity-Acceleration
  • Position-Time Graphs
  • Velocity-Time Graphs
  • Newton's First Law
  • Newton's Second Law
  • Newton's Third Law
  • Terminal Velocity
  • Projectile Motion
  • Forces in 2 Dimensions
  • Impulse and Momentum Change
  • Momentum Conservation
  • Work-Energy Fundamentals
  • Work-Energy Relationship
  • Roller Coaster Physics
  • Satellite Motion
  • Electric Fields
  • Circuit Concepts
  • Series Circuits
  • Parallel Circuits
  • Describing-Waves
  • Wave Behavior Toolkit
  • Standing Wave Patterns
  • Resonating Air Columns
  • Wave Model of Light
  • Plane Mirrors
  • Curved Mirrors
  • Teacher Guide
  • Using Lab Notebooks
  • Current Electricity
  • Light Waves and Color
  • Reflection and Ray Model of Light
  • Refraction and Ray Model of Light
  • Classes (Legacy)
  • Teacher Resources
  • Subscriptions

problem solving electrical circuit

  • Newton's Laws
  • Einstein's Theory of Special Relativity
  • About Concept Checkers
  • School Pricing
  • Newton's Laws of Motion
  • Newton's First Law
  • Newton's Third Law

Electricity: Electric Circuits

Electric circuits: problem set overview.

There are 15 ready-to-use problem sets on the topic of Electric Circuits. The problems target your ability to use circuit concepts and equations to analyze simple circuits, series circuits, parallel circuits, and combination circuits. Problems range in difficulty from the very easy and straight-forward to the very difficult and complex.   

When charge flows through the wires of an electric circuit , current is said to exist in the wires. Electric current is a quantifiable notion that is defined as the rate at which charge flows past a point on the circuit. It can be determined by measuring the quantity of charge that flows past a cross-sectional area of a wire on the circuit. As a rate quantity, current ( I ) is expressed by the following equation

where Q is the quantity of charge flowing by a point in a time period of t . The standard metric unit for the quantity current is the ampere, often abbreviated as Amps or A. A current of 1 ampere is equivalent to 1 Coulomb of charge flowing past a point in 1 second. Since the quantity of charge passing a point on a circuit is related to the number of mobile charge carriers (electrons) which flow past that point, the current can also be related to the number of electrons and the time. To make this connection between the current and the number of electrons, one must know the quantity of charge on a single electron.

Q electron = 1.6 x 10 -19 C

As charge flows through a circuit, it encounters resistance or a hindrance to its flow. Like current, resistance is a quantifiable term. The quantity of resistance offered by a section of wire depends upon three variables - the material the wire is made out of, the length of the wire, and the cross-sectional area of the wire. One physical property of a material is its resistivity - a measure of that material's tendency to resist charge flow through it. Resistivity values for various conducting materials are typically listed in textbooks and reference books. Knowing the resistivity value ( ρ ) of the material the wire is composed of and its length ( L ) and cross-sectional area ( A ), its resistance ( R ) can be determine using the equation below.

R = ρ • L / A

The standard metric unit of resistance is the ohm (abbreviated by the Greek letter Ω ).

The main difficulty with the use of the above equation pertains to the units of expression of the various quantities. The resistivity ( ρ ) is typically expressed in ohm•m. Thus, the length should be expressed in units of m and the cross-sectional area in m 2 . Many wires are round and have a circular cross-section. As such, the cross-sectional area in the above equation can be calculated from knowledge of the wire's radius or diameter using the formula for the area of a circle.

A = π • R 2 = π • D 2 / 4

Use our video on Electric Resistance fo solidfy your understanding of these resistance formulas.  

Voltage-Current-Resistance Relationship

The amount of current that flows in a circuit is dependent upon two variables. Current is inversely proportional to the overall resistance ( R ) of the circuit and directly proportional to the electric potential difference impressed across the circuit. The electric potential difference ( ΔV ) impressed across a circuit is simply the voltage supplied by the energy source (batteries, outlets, etc.). For homes in the United States, this value is close to 110-120 Volts. The mathematical relationship between current ( I ), voltage and resistance is expressed by the following equation (which is sometimes referred to as the Ohm's law equation ).

Electrical circuits are all about energy. Energy is put into a circuit by the battery or the commercial electricity supplier. The elements of the circuit (lights, heaters, motors, refrigerators, and even wires) convert this electric potential energy into other forms of energy such as light energy, sound energy, thermal energy and mechanical energy. Power refers to the rate at which energy is supplied or converted by the appliance or circuit. It is the rate at which energy is lost or gained at any given location within the circuit. As such, the generic equation for power is

P = ΔE / t

The energy loss (or gain) is simply the product of the electric potential difference between two points and the quantity of charge which moves between those two points in a time period of t. As such, the energy loss (or gain) is simply ΔV • Q . When this expression is substituted into the above equation, the power equation becomes

P = ΔV • Q / t

Since the Q/t ratio found in the above equation is equal to the current ( I ), the above equation can also be written as

P = ΔV • I

By combining the Ohm's law equation with the above equation, two other power equations can be generated. They are

• R / R

The standard metric unit of power is the Watt . In terms of units, the Watt is equivalent to an Amp•Volt, an Amp 2 •Ohm, and a Volt 2 /Ohm. Our video on Electric Power Equations will discuss these formulae in greater detail.  

Electricity Costs

A commercial power company charges households for the energy supplied on a monthly basis. The bill for the services typically states the amount of energy consumed during the month in units of kiloWatt•hours . This unit - a power unit multiplied by a time unit - is a unit of energy. A household typically pays the bill on the basis of the number of kW•hr of electrical energy consumed during the month. Thus, the task of determining the cost of using a specific appliance for a specified period of time is quite straightforward. The power must first be determined and converted to kiloWatts. This power must then be multiplied by the usage time in hours to obtain the energy consumed in units of kW•hr. Finally, this energy amount must be multiplied by the cost of electricity on a $/kW•hr basis in order to determine the cost in dollars.  

It is quite common that a circuit consist of more than one resistor. While each resistor has its own individual resistance value, the overall resistance of the circuit is different than the resistance of the individual resistors which make up the circuit. A quantity known as the equivalent resistance indicates the total resistance of the circuit. Conceptually, the equivalent resistance is the resistance that a single resistor would have in order to produce the same overall effect on the resistance as the combination of resistors that are present. So if a circuit has three resistors with an equivalent resistance of 25 ohm, then a single 25-ohm resistor could replace the three individual resistors and have the equivalent effect upon the circuit. The value of the equivalent resistance ( R eq ) takes into consideration the individual resistance values of the resistors and the way in which those resistors are connected.

There are two basic ways in which resistors can be connected in an electrical circuit. They can be connected in series or in parallel . Resistors that are connected in series are connected in consecutive fashion such that all the charge that passes through the first resistor will also pass through the other resistors. In series connection, all of the charge flowing through the circuit passes through each one of the individual resistors. As such, the equivalent resistance of series-connected resistors is the sum of the individual resistance values of those resistors.

R eq = R 1 + R 2 + R 3 + … (series connections)

Resistors that are connected in parallel are connected in side-by-side fashion such that the charge approaching the resistors will split up into two or more different paths. Parallel-connected resistors are characterized as having branching locations where charge branches off into the different pathways. The charge which passes through one resistor will not pass through the other resistors. The equivalent resistance of parallel-connected resistors is less than the resistance values of all the individual resistors in the circuit. While it may not be entirely intuitive, the equation for the equivalent resistance of parallel-connected resistors is given by an equation with several reciprocal terms.

1/R eq = 1/R 1 + 1/R 2 + 1/R 3 + … (parallel connections)

Series Circuit Analysis

Several of the problems in this unit pertain to series circuits. It is not unusual that a problem be accompanied by a drawing or a schematic diagram showing the arrangement of batteries and resistors. The drawing and corresponding schematic diagram below represents a series circuit powered by three cells and having three series-connected resistors (light bulbs).

problem solving electrical circuit

By imagining a charge leaving the positive terminal of the battery and following its path as it traverses the complete loop, it becomes evident that the charge goes through every resistor in consecutive fashion. As such it meets the criteria of a series circuit. Knowing that the circuit is a series circuit, allows you to relate the overall or equivalent resistance of the circuit to the individual resistance values by the equivalent resistance equation discussed above.

The current of a series circuit is the same in the resistors as it is in the battery. Since there is no branching off locations where charge divides into pathways, it can be stated that the current in the battery is equal to the current in resistor 1 is equal to the current in resistor 2 and is equal to the current in resistor 3 ... . In equation form, it can be written that

I battery = I 1 = I 2 = I 3 = … (series circuits)

As charge traverses the resistors of a series circuit, there is a drop in electric potential as it passes through each resistor. This drop in electric potential across each resistor is determined by the current through the resistor and the resistance of the resistor. This is consistent with the Ohm's law equation described above ( ΔV = I • R ). Since the current ( I ) in each individual resistor is the same, it is logical to conclude that the resistors with the greatest resistance ( R ) will have the greatest electric potential difference ( ΔV ) impressed across them.

The electric potential difference across the individual resistors of a circuit is often referred to as a voltage drop . These voltage drops of the series-connected resistors are mathematically related to the electric potential or voltage rating of the cells or battery which power the circuit. If a charge gains 12 volts of electric potential as it passes through the battery of an electric circuit, then it will lose 12 V as it passes through the external circuit. This 12 V drop in electric potential results from a series of individual drops in electric potential as it passes through the individual resistors of the series circuit. These individual voltage drops (electric potential difference) add up to give the total voltage drop of the circuit, In equation form, It can be said that

ΔV battery = ΔV 1 + ΔV 2 + ΔV 3 + … (series circuits)

where ΔV battery is the electric potential gained in the battery and ΔV 1 , ΔV 2 and ΔV 3 are the voltage drops (or electric potential differences) across the individual resistors.

A more detailed and exhaustive discussion of series circuits and their analysis can be found at The Physics Classroom Tutorial . And our videos on Series Circuit Relationships and Series Circuit Analysis will be very helpful.  

Parallel Circuit Analysis

Several problems in this unit pertain to parallel circuits. Again, it is not unusual that a problem be accompanied by a drawing or a schematic diagram showing the arrangement of batteries and resistors. The drawing and corresponding schematic diagram below represents a parallel circuit powered by three cells and having three parallel-connected resistors (light bulbs).

problem solving electrical circuit

By imagining a charge leaving the positive terminal of the battery and following its path as it traverses the complete loop, it becomes evident that the charge reaches a branching location (a  node ) prior to reaching a resistor. At the branching location sometimes referred to as a node, charge follows one of the three possible paths through the resistors. Rather than pass through every resistor, a single charge will pass through a single resistor during a complete loop around the circuit. As such it meets the criteria of a parallel circuit. Knowing that the circuit is a parallel circuit, allows you to relate the overall or equivalent resistance of the circuit to the individual resistance values by the equivalent resistance equation discussed above.

At the branching location, charge is splitting into separate pathways. As such, the current in the individual pathways will be less than the current outside the pathways. The overall current flow in the circuit and the current in the battery is equal to the sum of the current in the individual pathways. In equation form, it can be written that

I battery = I 1 + I 2 + I 3 + … (parallel circuits)

The current values of these individual branches are controlled by two quantities - the resistance of the resistor in the branch and the electric potential difference (ΔV) impressed across the branch. Consistent with Ohm's law equation discussed above, it can be said that the current in branch 1 is equal to the electric potential difference across branch 1 divided by the resistance of branch 1. Similar statements can be made of the other branches. In equation form, it can be stated that

= ΔV / R = ΔV / R = ΔV / R

The electic potential differences ( ΔV 1 , ΔV 2 and ΔV 3 ) across the individual resistors are often referred to as voltage drops. Similar to series circuits, any charge leaving the battery must encounter the same drop in voltage as the gain that it encounters when passing through the battery. But unlike series circuits, a charge in a parallel circuit will only pass through one resistor. As such, the voltage drop across that resistor must equal the electric potential difference across the battery. In equation form, it can be stated that

ΔV battery = ΔV 1 = ΔV 2 = ΔV 3 + … (parallel circuits)

A more detailed and exhaustive discussion of parallel circuits and their analysis can be found at The Physics Classroom Tutorial . And our videos on Parallel Circuit Relationships and Parallel Circuit Analysis will be very helpful.  

Habits of an Effective Problem-Solver

An effective problem solver by habit approaches a physics problem in a manner that reflects a collection of disciplined habits. While not every effective problem solver employs the same approach, they all have habits which they share in common. These habits are described briefly here. An effective problem-solver...

  • ...reads the problem carefully and develops a mental picture of the physical situation. If needed, they sketch a simple diagram of the physical situation to help visualize it.
  • ...identifies the known and unknown quantities and records them in an organized manner, often times recording them on the diagram itself. They equate given values to the symbols used to represent the corresponding quantity (e.g., ΔV = 9.0 V; R = 0.025 Ω; I = ???).
  • ...plots a strategy for solving for the unknown quantity; the strategy will typically center around the use of physics equations and be heavily dependent upon an understanding of physics principles.
  • ...identifies the appropriate formula(s) to use, often times writing them down. Where needed, they perform the needed conversion of quantities into the proper unit.
  • ...performs substitutions and algebraic manipulations in order to solve for the unknown quantity.

Read more...  

Additional Readings/Study Aids:

The following pages from The Physics Classroom Tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.

  • Electric Potential Difference
  • Electric Current
  • Power: Putting Charges to Work
  • Ohm's Law
  • Power Revisited
  • Combination Circuits

Watch a Video

We have developed and continue to develop Video Tutorials on introductory physics topics. You can find these videos on our YouTube channel . We have an entire Playlist on the topic of Electric Circuits .  

Physics Problems with Solutions