Ohm's Law Examples: 45 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Ohm's Law.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The fundamental relationship stating that the voltage ( $V$ ) across an ohmic conductor equals the current ( $I$ ) flowing through it multiplied by its resistance ( $R$ ).

More push (voltage) means more flow (current). More resistance means less flow for the same push.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Ohm's Law asks students to follow the circuit path and identify what quantity changes at each component.

Common stuck point: Students often know a formula related to ohm's law but skip the recognition step: Can I identify the circuit path, what quantity is flowing or changing, and which electrical rule links the quantities? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Can I identify the circuit path, what quantity is flowing or changing, and which electrical rule links the quantities?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Electric Current Mistakes

Worked Examples

Example 1

easy

12 \text{ V}

battery is connected to a

4 \text{ } \Omega

resistor. What current flows?

Answer

I = 3 A

First step

Apply Ohm's law:

I = \frac{V}{R}

Full solution

2
Substitute the values: $I = \frac{12}{4}$ .
3
$I = 3 A$

Ohm's law (

V = IR

) is the fundamental relationship in circuit analysis. It connects voltage, current, and resistance in a simple linear relationship.

Example 2

medium

A heater draws

5 \text{ A}

from a

240 \text{ V}

supply. What is its resistance, and how much power does it consume?

Example 3

medium

A wire's resistance is

2 \text{ } \Omega

at low current. When the wire heats up and its resistance rises to

3 \text{ } \Omega

, what current flows under a fixed

6 \text{ V}

supply (before and after)?

Example 4

medium

An ohmic device shows a straight

V

–

I

line passing through

(2 \text{ A}, 5 \text{ V})

and

(6 \text{ A}, 15 \text{ V})

. What is its resistance?

Example 5

medium

9 \text{ V}

battery drives a current of

30 \text{ mA}

through a resistor. Find (a) the resistance and (b) the power dissipated.

Example 6

hard

A wire of resistance

5 \text{ } \Omega

is replaced by a wire of the same material with half the length and double the cross-sectional area. What is the new resistance, and what current will it draw at

10 \text{ V}

Example 7

hard

Two resistors of

6 \text{ } \Omega

and

3 \text{ } \Omega

are connected in parallel across a

12 \text{ V}

battery. Use Ohm's law to find the current in each resistor and the total current.

Example 8

challenge

An ohmic resistor obeys

V = IR

with

R = 50 \text{ } \Omega

. A time-varying voltage

V(t) = 10\sin(100 t) \text{ V}

is applied. Write

I(t)

and find the peak current.

Example 9

hard

A copper wire carries

2 \text{ A}

when

0.1 \text{ V}

is applied across its ends. What is its resistance? If the wire is stretched (at constant volume) so its length doubles, what is the new resistance?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

What voltage is needed to push

0.25 \text{ A}

through a

100 \text{ } \Omega

resistor?

Example 2

medium

A resistor in a circuit has a current of

0.5 \text{ A}

flowing through it when connected to a

6 \text{ V}

supply. (a) What is its resistance? (b) If the voltage is doubled to

12 \text{ V}

, what is the new current (assuming constant resistance)?

Example 3

easy

State Ohm's law relating voltage, current, and resistance.

Example 4

easy

6\,\Omega

resistor carries

2

A. What voltage is across it?

Example 5

easy

10

V source drives a

5\,\Omega

resistor. What current flows?

Example 6

easy

A resistor has

9

V across it and

3

A through it. Find its resistance.

Example 7

easy

Does Ohm's law

V=IR

apply exactly to a normal filament light bulb at all currents?

Example 8

easy

Convert before using Ohm's law: a resistor of

2

\Omega

carries

3

mA. What units must you use first?

Example 9

easy

If voltage across an ohmic resistor doubles, what happens to the current?

Example 10

easy

12

V battery is connected to a

4\,\Omega

resistor. What is the current?

Example 11

medium

24

V battery drives two series resistors

3\,\Omega

and

5\,\Omega

. What current flows?

Example 12

medium

In a series circuit,

2

A flows through a

7\,\Omega

resistor. What is the voltage drop across it?

Example 13

medium

20

V source feeds a

6\,\Omega

and

4\,\Omega

resistor in parallel. What is the total current from the source?

Example 14

medium

A resistor dissipates when

4

A passes and the drop is

8

V. Verify its resistance and find the voltage if current rises to

6

Example 15

medium

A wire carries

0.5

A under

1.5

V. What current flows if voltage increases to

4.5

V (ohmic)?

Example 16

medium

A student computes current as

I = V \times R

and gets

200

A for

10

V and

20\,\Omega

. What is wrong, and the correct current?

Example 17

medium

A circuit has a

9

V battery and a current of

0.6

A. What single resistance would produce this?

Example 18

challenge

30

V source feeds a

4\,\Omega

resistor in series with a parallel pair of

6\,\Omega

and

3\,\Omega

. Find the current from the source.

Example 19

challenge

Two resistors in series carry the same current. The

3\,\Omega

resistor drops

6

V. What is the drop across the

5\,\Omega

resistor?

Example 20

challenge

A resistor's voltage and current are measured:

(2\text{ V}, 1\text{ A})

and

(6\text{ V}, 2\text{ A})

. Is this device ohmic?

Example 21

medium

15

V source drives

2\,\Omega

and

3\,\Omega

in series. Find the current.

Example 22

medium

A resistor passes

3

A under

6

V. What current flows at

18

V (ohmic)?

Example 23

easy

A current of

0.4 \text{ A}

flows through a

25 \text{ } \Omega

resistor. What voltage is across it?

Example 24

easy

A resistor has

15 \text{ V}

across it and

5 \text{ A}

through it. What is its resistance?

Example 25

easy

1.5 \text{ V}

AA cell drives a

30 \text{ } \Omega

bulb (treat as ohmic). Find the current.

Example 26

medium

4.7 \text{ k}\Omega

resistor is connected to a

9 \text{ V}

battery. What current (in mA) flows?

Example 27

medium

A wall socket supplies

120 \text{ V}

to a toaster that draws

8 \text{ A}

. What is the toaster's effective resistance?

Example 28

medium

Two resistors are tested under the same

12 \text{ V}

supply. Resistor A draws

0.6 \text{ A}

; resistor B draws

1.2 \text{ A}

. Which has larger resistance, and by what factor?

Example 29

medium

220 \text{ V}

kettle has a heating element of resistance

44 \text{ } \Omega

. What current does it draw?

Example 30

medium

If the voltage across an ohmic resistor increases by

50\%

, by what percentage does the current change?

Example 31

hard

A resistor dissipates

4.0 \text{ W}

when

2.0 \text{ A}

flows through it. What is its resistance, and what voltage is across it?

Example 32

hard

A student plots

V

I

for a thermistor and gets a curve that flattens at high current. Does the thermistor obey Ohm's law? Justify with one sentence.

Example 33

hard

1.2 \text{ V}

cell with internal resistance

0.3 \text{ } \Omega

drives a

0.9 \text{ } \Omega

external resistor. What current flows, and what voltage appears across the external resistor?

Example 34

hard

A microcontroller pin outputs

3.3 \text{ V}

and is connected through a series resistor to an LED that drops

2.0 \text{ V}

at the desired current of

10 \text{ mA}

. What resistor value is needed?

Example 35

medium

A resistor labelled

"5\%, 100 \text{ } \Omega"

is connected to a

5 \text{ V}

supply. Give the minimum and maximum currents consistent with the tolerance.

Example 36

challenge

Two ohmic resistors in series have resistances in ratio

2:3

. The voltage across the second resistor is

9 \text{ V}

. What is the voltage across the first resistor, and the total supply voltage?

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Related Concepts

Voltage Resistance Electric Current Series Circuit Parallel Circuit Electrical Power

Background Knowledge

These ideas may be useful before you work through the harder examples.

voltageresistanceelectric current