Voltage Examples: 44 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Voltage.

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 difference in electric potential energy per unit charge between two points. Measured in volts (V).

Voltage is like water pressure — it's the 'push' that drives current through a circuit.

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: Voltage 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 voltage 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

A battery does

24 \text{ J}

of work to move

6 \text{ C}

of charge. What is the voltage of the battery?

Answer

V = 4 V

First step

Voltage is work done per unit charge:

V = \frac{W}{Q}

Full solution

2
Substitute the values: $V = \frac{24}{6}$ .
3
$V = 4 V$

Voltage (potential difference) is the energy transferred per coulomb of charge. A higher voltage means more energy per charge, driving more current through a circuit.

Example 2

medium

12 \text{ V}

battery drives a current of

2 \text{ A}

for

30 \text{ s}

. How much energy does it supply?

Example 3

medium

12 \text{ V}

battery is connected across a

4 \text{ }\Omega

resistor. Find the current and power dissipated.

Example 4

medium

An electron (

q = 1.6 \times 10^{-19} \text{ C}

) is accelerated through

1000 \text{ V}

. Find the kinetic energy gained.

Example 5

hard

A battery has emf

12 \text{ V}

and internal resistance

0.5 \text{ }\Omega

. When connected to a

5.5 \text{ }\Omega

load, find the terminal voltage.

Example 6

medium

Two parallel plates separated by

2 \text{ mm}

create a uniform electric field

E = 5000 \text{ V/m}

. Find the voltage across the plates.

Example 7

hard

A capacitor of

10 \text{ }\mu\text{F}

stores

5 \text{ mJ}

of energy. Find the voltage across it.

Example 8

challenge

In a Kirchhoff loop, three batteries of

6, 4, 2 \text{ V}

are arranged so the

2 \text{ V}

source opposes the others. Total resistance is

4 \text{ }\Omega

. Find the loop current.

Example 9

medium

A point in an electric field has potential

+8 \text{ V}

; another point has

-2 \text{ V}

. Find the work done by the field on a

+3 \text{ C}

charge moving from the first to the second.

Example 10

hard

A potential divider has

R_1 = 1 \text{ k}\Omega

and

R_2 = 3 \text{ k}\Omega

in series across

12 \text{ V}

. Find the voltage across

R_2

Practice Problems

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

Example 1

easy

How much work does a

9 \text{ V}

battery do to push

4 \text{ C}

of charge through a circuit?

Example 2

medium

9 \text{ V}

battery transfers

450 \text{ J}

of energy to a circuit. How much charge has passed through the battery?

Example 3

easy

What is the SI unit of voltage?

Example 4

easy

Write the formula relating voltage, energy, and charge.

Example 5

easy

A charge of

2

C gains

10

J moving through a battery. What is the voltage?

Example 6

easy

Is voltage measured 'across' or 'through' a component?

Example 7

easy

A voltmeter reads

3

V across one resistor and

5

V across another in series. What is the total voltage across both?

Example 8

easy

Two parallel branches connect the same two nodes. One has

6

V across it. What voltage is across the other?

Example 9

easy

A battery is labeled

9

V. What does this number represent?

Example 10

easy

How much energy does

4

C gain across a

12

V source?

Example 11

medium

In a series loop, a

12

V battery drives two resistors. One drops

7

V. What does the other drop?

Example 12

medium

A charge of

0.5

C releases

6

J crossing a resistor. What is the voltage drop across it?

Example 13

medium

24

V source feeds three equal series resistors. What is the voltage across each?

Example 14

medium

10

V battery has

0.5

V lost to internal resistance. What is the terminal voltage?

Example 15

medium

Across a component,

3

C carries

36

J of energy. A student says the voltage is

108

V. What went wrong, and what is the correct value?

Example 16

medium

A series circuit has drops of

4

V_2

, and

3

V across three resistors, powered by a

15

V battery. Find

V_2

Example 17

medium

6

V supply pushes

2

A through a circuit for

5

s. How much energy is delivered?

Example 18

challenge

12

V battery with

1\,\Omega

internal resistance drives a

5\,\Omega

external resistor. What is the terminal voltage?

Example 19

challenge

In a loop, going around you encounter a

20

V battery (rise), then drops of

8

V and

V_x

, then a

4

V battery oriented as a drop. KVL gives what

V_x

Example 20

challenge

A charge moves through a

9

V rise then a

4

V drop then a

2

V drop in a path. What is the net energy gained per coulomb, and is this consistent with a closed loop?

Example 21

medium

A charge of

3

C gains

36

J crossing a source. Find the voltage.

Example 22

medium

A series loop has a

20

V battery and drops of

5

7

V, and

V_3

. Find

V_3

Example 23

easy

48 \text{ J}

of work moves

8 \text{ C}

of charge across a battery. Find the voltage.

Example 24

easy

A current of

2 \text{ A}

flows through a

5 \text{ }\Omega

resistor. Find the voltage across it.

Example 25

medium

Two resistors of

4 \text{ }\Omega

and

8 \text{ }\Omega

in series share a total

24 \text{ V}

. Find the voltage across each.

Example 26

easy

1.5 \text{ V}

AA battery supplies

0.5 \text{ A}

for

20 \text{ s}

. How much energy is delivered?

Example 27

medium

A car battery delivers

50 \text{ A}

12 \text{ V}

when starting. Find the power.

Example 28

easy

9 \text{ V}

battery transfers

1 \text{ C}

of charge. How much work is done?

Example 29

medium

120 \text{ V}

outlet supplies a

1500 \text{ W}

heater. Find the current drawn.

Example 30

easy

5 \text{ V}

power supply delivers

0.2 \text{ A}

to a USB device. Find the power.

Example 31

medium

230 \text{ V}

kettle has resistance

46 \text{ }\Omega

. Find the current.

Example 32

medium

A voltmeter reads

3.7 \text{ V}

across a phone battery delivering

0.5 \text{ A}

. Find the power delivered.

Example 33

easy

A battery does

20 \text{ J}

of work moving

5 \text{ C}

of charge. Find the voltage.

Example 34

medium

An LED needs

2 \text{ V}

20 \text{ mA}

. Connected to a

5 \text{ V}

supply with a series resistor, what resistor value is required?

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Related Concepts

Electric Current Resistance Ohm's Law Potential Difference

Background Knowledge

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

electric current