Practice Kirchhoff's Laws in Physics

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

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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 V36\,\text{V} battery, a 4 Ω4\,\Omega resistor, and a 2 Ω2\,\Omega resistor in series. Use KVL to find the voltage drop across the 4 Ω4\,\Omega resistor.

Example 2

hard
A two-loop circuit shares a 5 Ω5\,\Omega branch. Loop 1 drives 3 A3\,\text{A} down through the shared branch; loop 2 drives 1 A1\,\text{A} up. Find the net current in the shared branch and its direction.

Example 3

medium
A node has 3 A3\,\text{A}, 5 A5\,\text{A} entering and 2 A2\,\text{A}, II leaving. Find II.

Example 4

medium
A junction has 66 A in, and two branches out: one carries 2.52.5 A. Find the other branch current.

Example 5

challenge
A loop contains a 12 V12\,\text{V} battery and an internal resistance r=0.5 Ωr = 0.5\,\Omega, plus an external 5.5 Ω5.5\,\Omega resistor. Use KVL to find the current and the terminal voltage.

Example 6

medium
A node has currents I1=3 AI_1 = 3\,\text{A} in, I2=1 AI_2 = 1\,\text{A} out, and I3I_3 in. The only fourth branch carries 5 A5\,\text{A} out. Find I3I_3.

Example 7

medium
In a single-loop circuit, the sum of resistor drops is 18 V18\,\text{V}. What is the EMF of the only battery, if it is the only source?

Example 8

medium
A node analysis assumes a 33 A branch leaves, but balancing gives −3-3 A. What does the sign mean?

Example 9

easy
State Kirchhoff's current law (KCL).

Example 10

hard
A loop contains a 24 V24\,\text{V} battery, a 4 Ω4\,\Omega resistor in the outer loop, and an inner branch with 2 Ω2\,\Omega that also carries a known 1 A1\,\text{A} from a neighboring mesh, aiding the loop current. The loop KVL reads 24=4I+2(I+1)24 = 4 I + 2(I + 1). Find II.

Example 11

hard
Two batteries in series aid each other (6 V6\,\text{V} and 9 V9\,\text{V}) with three resistors in series (1 Ω1\,\Omega, 2 Ω2\,\Omega, 3 Ω3\,\Omega). Use KVL to find the loop current.

Example 12

easy
In a single loop with a 24 V24\,\text{V} battery, one resistor drops 9 V9\,\text{V} and another drops V2V_2. Find V2V_2.

Example 13

medium
Two batteries oppose each other in a loop: 1010 V rise and 66 V drop, with a single resistor. Find the resistor's drop.

Example 14

easy
A node has 7 A7\,\text{A} entering and two branches leaving with 4 A4\,\text{A} and II. Find II.

Example 15

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

Example 16

hard
A loop contains a 10 V10\,\text{V} battery and three parallel resistors (2 Ω2\,\Omega, 4 Ω4\,\Omega, 4 Ω4\,\Omega) connected across it. Using KCL at one node, find the total current drawn from the battery.

Example 17

medium
In a single loop, a 2020 V battery drives a 2 Ω2\,\Omega and a 3 Ω3\,\Omega resistor. Use KVL to find the current.

Example 18

challenge
At a node, three currents are defined as leaving: I1=4I_1 = 4 A, I2=−3I_2 = -3 A, I3=?I_3 = ?, with KCL I1+I2+I3=0I_1 + I_2 + I_3 = 0. Find I3I_3 and interpret its sign.

Example 19

medium
A node has 88 A in and branches of 33 A and II out. Find II.

Example 20

hard
In a two-mesh circuit, mesh 1 has KVL 12=4I1+2(I1−I2)12 = 4 I_1 + 2(I_1 - I_2) and mesh 2 has −6=3I2+2(I2−I1)-6 = 3 I_2 + 2(I_2 - I_1). Solve for I1I_1 and I2I_2.
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