Ohm’s Law Problems With Answers and Full Working

Overview

The core relationship in these questions is Ohm’s law:

V = IR

where:

• V is voltage in volts (V)
• I is current in amperes or amps (A)
• R is resistance in ohms (Ω)

Most electricity practice questions at introductory level ask you to find one of these three quantities when the other two are known. That sounds simple, but the real challenge is usually one of these:

• choosing the correct formula form
• rearranging the equation without errors
• keeping track of units
• recognising whether the values are realistic
• connecting Ohm’s law to a larger circuit question

A reliable method helps more than memorising isolated answers. For almost every Ohm’s law question, use this routine:

1. Write down what is given.
2. Write down what you need to find.
3. Select the formula.
4. Rearrange if needed.
5. Substitute values with units.
6. Calculate carefully.
7. Check whether the result makes physical sense.

Here are worked examples across easy, medium, and mixed-question levels.

Worked example 1: Find the current

A resistor has a resistance of 5 Ω and a voltage of 10 V across it. Find the current.

Step 1: Identify known values
V = 10 V
R = 5 Ω

Step 2: Identify the unknown
I = ?

Step 3: Use Ohm’s law
V = IR

Step 4: Rearrange for current
I = V / R

Step 5: Substitute
I = 10 / 5

Step 6: Calculate
I = 2 A

Answer: The current is 2 A.

Worked example 2: Find the resistance

A current of 3 A flows through a component when the voltage across it is 12 V. Find the resistance.

Given:
V = 12 V
I = 3 A

Unknown:
R = ?

Formula:
V = IR

Rearrange:
R = V / I

Substitute:
R = 12 / 3

Calculate:
R = 4 Ω

Answer: The resistance is 4 Ω.

Worked example 3: Find the voltage

A resistor of 8 Ω carries a current of 0.5 A. Find the voltage across it.

Given:
R = 8 Ω
I = 0.5 A

Unknown:
V = ?

Formula:
V = IR

Substitute:
V = 0.5 × 8

Calculate:
V = 4 V

Answer: The voltage is 4 V.

These first examples are straightforward, but the same method scales to harder questions. In exam settings, students often lose marks not because the physics is advanced, but because they skip the structure.

Topic map

This section shows the main types of Ohm’s law questions you are likely to meet, with examples and solution habits for each one.

1. Direct substitution questions

These are the simplest. You are given two of V, I, and R, and you find the third.

Practice question:
A lamp has a resistance of 20 Ω and the current through it is 0.3 A. Find the voltage.

Solution:
Use V = IR
V = 0.3 × 20 = 6 V

Answer: 6 V

Tip: Always copy the unit with each value before calculating.

2. Rearrangement questions

These test algebra as much as physics.

Practice question:
A device operates at 24 V and draws a current of 0.8 A. Find its resistance.

Solution:
Given V = 24 V, I = 0.8 A
Use V = IR
Rearrange: R = V / I
R = 24 / 0.8 = 30 Ω

Answer: 30 Ω

Tip: If algebra feels slow, write the formula triangle only as a temporary support, but aim to understand the rearrangement properly.

3. Decimal and unit-care questions

These become harder when the numbers are less tidy.

Practice question:
A resistor has a resistance of 47 Ω and a current of 0.12 A flows through it. Find the voltage.

Solution:
V = IR
V = 47 × 0.12 = 5.64 V

Answer: 5.64 V

Tip: Keep enough significant figures during the calculation, then round only if your course expects it.

4. Reverse-check questions

Sometimes you are asked whether a stated value is correct.

Practice question:
A student says that for a 9 V battery connected to a 3 Ω resistor, the current is 1 A. Is the student correct?

Solution:
Use I = V / R
I = 9 / 3 = 3 A

The claim of 1 A is incorrect.

Answer: No. The correct current is 3 A.

Tip: These questions reward a quick calculation and a clear sentence, not just a number.

5. Multi-step circuit questions

Ohm’s law often appears inside a larger electricity problem. You may first need to identify the resistance of one section, total current, or voltage across a branch. If you are revising series and parallel circuits, it helps to pair this hub with Electric Circuits Explained: Series vs Parallel With Worked Examples.

Practice question:
A 12 V supply is connected to a resistor, and the current is measured as 2 A. The resistor is then replaced with another resistor and the current drops to 0.5 A. What is the new resistance?

Solution:
For the new resistor:
V = 12 V
I = 0.5 A
R = V / I = 12 / 0.5 = 24 Ω

Answer: 24 Ω

6. Worded exam-style questions

These are where students often hesitate because the equation is hidden inside the wording.

Practice question:
An electric heater draws 5 A from a 230 V supply. What is its resistance?

Solution:
Known values:
V = 230 V
I = 5 A

Use R = V / I

R = 230 / 5 = 46 Ω

Answer: 46 Ω

Tip: Translate the words into a short data list before touching the formula.

7. Spotting common mistakes

Here are errors that appear again and again in Ohm’s law worked examples:

• using multiplication when division is needed
• confusing current with voltage
• forgetting units
• copying values incorrectly from the question
• rearranging the formula badly
• giving an answer with the wrong unit, such as volts instead of ohms

A useful self-check is this: if resistance gets larger while voltage stays the same, current should get smaller. If your answer says the opposite, check the calculation again.

Related subtopics

Ohm’s law is a foundation, not an isolated topic. Once you are comfortable with direct voltage-current-resistance problems, the next useful step is to connect it with the wider electricity unit.

Power in electric circuits

Many problems combine Ohm’s law with electrical power:

• P = VI
• P = I²R
• P = V² / R

For example, if a resistor has 6 V across it and a current of 2 A, then the power is:

P = VI = 6 × 2 = 12 W

This type of crossover appears often in GCSE, A-Level, AP Physics, and introductory college physics.

Series and parallel circuits

In real exam questions, you may need to calculate total resistance, branch current, or voltage across components before applying Ohm’s law to one part of the circuit. For that reason, this topic naturally connects with series and parallel circuit worked examples.

Current, charge, and time

Another useful link is the formula:

Q = It

If you know current and time, you can find charge. In mixed electricity questions, you may use one formula to find current first, then another to continue the problem.

Resistivity and material properties

At a more advanced level, resistance is not just a number in a question. It depends on a material’s resistivity, length, and cross-sectional area. That means Ohm’s law can open into deeper physical understanding: why some materials conduct better, why wires heat up, and why changing a component changes the whole circuit behaviour.

General problem-solving habits in physics

If you struggle less with the formula and more with the overall process, building a broader step-by-step physics routine can help. That is the same skill used in mechanics, forces, and motion. For example, if you also revise dynamics, you may find it useful to compare your workflow with Newton’s Laws of Motion Problems With Step-by-Step Solutions or revisit a wider reference page such as Physics Formulas Cheat Sheet: The Essential Equations Students Keep Forgetting.

The pattern is the same across topics: define the knowns, define the unknown, select the model, show the substitution, and check the result.

How to use this hub

This page works best if you use it actively rather than reading straight through once. The goal is to turn Ohm’s law questions and answers into repeatable habits.

1. Start with one difficulty level

If you are new to the topic, begin with direct substitution questions. Do not jump immediately to mixed circuit problems. Build accuracy first.

2. Cover the solution and attempt it yourself

Read only the question, pause, and solve it on paper. Then compare your method with the worked steps here. This is more effective than reading a solved example passively.

3. Say the units out loud

That may feel basic, but it helps. “Volts, amps, ohms” keeps each quantity in the right place and reduces mix-ups.

4. Keep an error log

Whenever you miss a question, write down why. Useful categories include:

• formula choice error
• rearrangement error
• calculator slip
• unit mistake
• misread wording

After a few sessions, patterns appear. That makes revision more efficient.

5. Use short sets for exam prep

Try three-question bursts:

1. one direct Ohm’s law problem
2. one rearrangement problem
3. one worded or mixed-context problem

This gives you variety without making revision feel heavy.

6. Link this topic to the bigger picture

If you can solve Ohm’s law questions but get lost in full circuit questions, revise the surrounding concepts next rather than repeating the same basic question type. The gap may not be the formula itself. It may be circuit structure.

7. Build your own mini formula sheet

Include:

• V = IR
• I = V / R
• R = V / I
• P = VI
• Q = It

Write one example beside each formula. This turns a formula sheet into a memory tool rather than a list.

8. Practise explaining one solution in full sentences

For instance: “I used Ohm’s law because the question gives voltage and current and asks for resistance. Rearranging V = IR gives R = V/I. Substituting 12 V and 3 A gives 4 Ω.” If you can explain the method clearly, you usually understand it well enough for exam conditions.

When to revisit

Come back to this hub whenever one of these happens:

• you start forgetting which form of Ohm’s law to use
• you can get answers but not with confident full working
• your course moves from simple component questions to full circuits
• you begin combining resistance questions with power, charge, or energy
• you notice the same mistakes repeating in homework or tests
• you need a quick revision page before an exam

A good revisit pattern is simple:

1. Week 1: Do three direct problems.
2. Week 2: Add three rearrangement problems.
3. Week 3: Add three worded questions.
4. Week 4: Add mixed circuit or power links.

If this hub expands over time, the most useful additions will usually be:

• more easy-to-hard question sets
• common exam traps
• mixed questions with power and series-parallel ideas
• short self-test sections without worked steps visible first

For now, the practical next step is this: pick two questions from this page, solve them without looking, then check every line of your working. If your method is clear and your units are correct, you are not just memorising Ohm’s law—you are learning how to solve physics problems reliably. That is the skill that carries into the rest of electricity and into physics more broadly.