Practice Kirchhoff's Laws in Physics

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Kirchhoff's laws are two rules for analyzing circuits. Kirchhoff's current law (junction rule) says the total current into any junction equals the total current out of it, because charge is conserved. Kirchhoff's voltage law (loop rule) says the sum of the voltage rises and drops around any closed loop is zero, because energy per unit charge is conserved.

Charge cannot pile up at a junction, and energy per unit charge must balance around a complete loop.

Showing a random 20 of 50 problems.

Example 1

medium

A loop has a

36\,\text{V}

battery, a

4\,\Omega

resistor, and a

2\,\Omega

resistor in series. Use KVL to find the voltage drop across the

4\,\Omega

resistor.

I = 6 A; V across 4 Ω

Example 2

hard

A two-loop circuit shares a

5\,\Omega

branch. Loop 1 drives

3\,\text{A}

down through the shared branch; loop 2 drives

1\,\text{A}

up. Find the net current in the shared branch and its direction.

Example 3

medium

A node has

3\,\text{A}

5\,\text{A}

entering and

2\,\text{A}

I

leaving. Find

I

KCL: 3+5

Example 4

medium

A junction has

6

A in, and two branches out: one carries

2.5

A. Find the other branch current.

KCL: 6 A

Example 5

challenge

A loop contains a

12\,\text{V}

battery and an internal resistance

r = 0.5\,\Omega

, plus an external

5.5\,\Omega

resistor. Use KVL to find the current and the terminal voltage.

KVL: I = 12/(0.5+5.5) = 2 A; V_term

Example 6

medium

A node has currents

I_1 = 3\,\text{A}

in,

I_2 = 1\,\text{A}

out, and

I_3

in. The only fourth branch carries

5\,\text{A}

out. Find

I_3

KCL: 3 + I₃

Example 7

medium

In a single-loop circuit, the sum of resistor drops is

18\,\text{V}

. What is the EMF of the only battery, if it is the only source?

KVL: EMF = total drop

Example 8

medium

A node analysis assumes a

3

A branch leaves, but balancing gives

-3

A. What does the sign mean?

Example 9

easy

State Kirchhoff's current law (KCL).

Example 10

hard

A loop contains a

24\,\text{V}

battery, a

4\,\Omega

resistor in the outer loop, and an inner branch with

2\,\Omega

that also carries a known

1\,\text{A}

from a neighboring mesh, aiding the loop current. The loop KVL reads

24 = 4 I + 2(I + 1)

. Find

I

Example 11

hard

Two batteries in series aid each other (

6\,\text{V}

and

9\,\text{V}

) with three resistors in series (

1\,\Omega

2\,\Omega

3\,\Omega

). Use KVL to find the loop current.

KVL: I

Example 12

easy

In a single loop with a

24\,\text{V}

battery, one resistor drops

9\,\text{V}

and another drops

V_2

. Find

V_2

KVL: 9 V + V₂

Example 13

medium

Two batteries oppose each other in a loop:

10

V rise and

6

V drop, with a single resistor. Find the resistor's drop.

Example 14

easy

A node has

7\,\text{A}

entering and two branches leaving with

4\,\text{A}

and

I

. Find

I

KCL: 7 A

Example 15

easy

Around any closed loop the algebraic sum of EMFs and IR drops equals ____.

Example 16

hard

A loop contains a

10\,\text{V}

battery and three parallel resistors (

2\,\Omega

4\,\Omega

4\,\Omega

) connected across it. Using KCL at one node, find the total current drawn from the battery.

KCL: I_total

Example 17

medium

In a single loop, a

20

V battery drives a

2\,\Omega

and a

3\,\Omega

resistor. Use KVL to find the current.

KVL: 20

Example 18

challenge

At a node, three currents are defined as leaving:

I_1 = 4

I_2 = -3

I_3 = ?

, with KCL

I_1 + I_2 + I_3 = 0

. Find

I_3

and interpret its sign.

Example 19

medium

A node has

8

A in and branches of

3

A and

I

out. Find

I

KCL: 8 A

Example 20

hard

In a two-mesh circuit, mesh 1 has KVL

12 = 4 I_1 + 2(I_1 - I_2)

and mesh 2 has

-6 = 3 I_2 + 2(I_2 - I_1)

. Solve for

I_1

and

I_2

← Back to Kirchhoff's Laws Worked Examples Formula Explained

Related Concepts

Circuit Series Circuit Parallel Circuit Electrical Power