Practice Potential Difference in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The difference in electric potential between two points, equal to the work done per unit charge moving between them.

Potential difference is the 'height drop' that makes charges flow — the bigger the drop, the harder the push.

Showing a random 20 of 50 problems.

Example 1

easy

Points A and B have potentials

12

V and

5

V. Find

V_A - V_B

Example 2

easy

Is potential difference a value at one point or between two points?

Example 3

medium

A field

E=400

N/C spans

d=0.25

m. A

2

C charge crosses it. Find the work done on the charge.

Example 4

challenge

In a uniform field, point A is at

20

V and B at

5

V, separated by

0.3

m along the field. Find both the field strength and the work to move

+2

C from A to B.

Example 5

medium

A point charge

Q = +5 \text{ nC}

sits at the origin. Find the potential difference

V(0.10 \text{ m}) - V(0.50 \text{ m})

along a radial line. Use

k = 9.0 \times 10^9 \text{ N m}^2/\text{C}^2

Example 6

easy

9

V battery moves

2

C. Find the energy delivered.

Example 7

medium

Two points A and B in an electric field have potentials

V_A = 100 \text{ V}

and

V_B = 40 \text{ V}

. What is the potential difference from A to B? How much work is done moving a

2 \times 10^{-6} \text{ C}

charge from B to A?

Example 8

hard

A uniform field

E = 800 \text{ V/m}

points in the

+x

direction. Find

V_B - V_A

if A is at

(0, 0)

and B is at

(0.05 \text{ m}, 0.10 \text{ m})

Example 9

easy

Moving a

+2 \text{ C}

charge from A to B against the field requires

24 \text{ J}

of external work. What is

V_B - V_A

Example 10

easy

A battery has a potential difference of

9 \text{ V}

across its terminals. How much energy does it give to each coulomb of charge that passes through it?

Example 11

challenge

A spherical conductor of radius

R = 0.10 \text{ m}

carries total charge

Q = +20 \text{ nC}

. Find the potential difference between its surface and a point at

r = 0.30 \text{ m}

from the center. Use

k = 9.0 \times 10^9 \text{ N m}^2/\text{C}^2

Example 12

medium

A uniform field gives

\Delta V = 60

V across

d=0.2

m. Find the field strength.

Example 13

hard

12 \text{ V}

battery with internal resistance

0.5 \text{ }\Omega

delivers current to an external

5.5 \text{ }\Omega

load. Find the terminal voltage across the battery.

Battery with internal resistance — find terminal voltage

Example 14

hard

In a circuit with a

12 \text{ V}

battery, three resistors in series have values

2 \text{ } \Omega

4 \text{ } \Omega

, and

6 \text{ } \Omega

. What is the potential difference across each? Verify that they sum to the battery voltage.

Series resistors across a 12 V battery

Example 15

medium

Two parallel resistors of

3 \text{ }\Omega

and

6 \text{ }\Omega

are connected across a

12 \text{ V}

source. What is the potential difference across each resistor?

Parallel resistors across a 12 V source

Example 16

challenge

A proton (

q=1.6\times10^{-19}

m=1.67\times10^{-27}

kg) starts at rest and is accelerated through

200

V. Find its final speed.

Example 17

medium

To move

5

C from A to B requires

40

J against the field. Find

V_B - V_A

Example 18

challenge

An alpha particle (

q = 2e = 3.2 \times 10^{-19} \text{ C}

m = 6.64 \times 10^{-27} \text{ kg}

) is accelerated from rest through

5000 \text{ V}

. Find its final speed.

Example 19

medium

+2

C charge moves from a point at

3

V to a point at

8

V. Find the work done by the field on it.

Example 20

hard

Two point charges

+4 \text{ nC}

and

-2 \text{ nC}

sit at

x = 0

and

x = 0.20 \text{ m}

respectively. Find the electric potential at

x = 0.10 \text{ m}

. Use

k = 9.0 \times 10^9 \text{ N m}^2/\text{C}^2

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Related Concepts

Electric Potential Voltage