Practice Parallel Circuit in Physics

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

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Quick Recap

A parallel circuit connects components in separate branches between two common nodes, so each component gets the full source voltage.

Like a river splitting into branches — the water (current) divides, but the pressure drop (voltage) across each branch is the same.

Showing a random 20 of 50 problems.

Example 1

easy
In a parallel circuit, what stays the same across each branch?

Example 2

medium
A 9 V9 \text{ V} battery is across three parallel resistors of 3 Ω3 \text{ } \Omega, 6 Ω6 \text{ } \Omega, and 9 Ω9 \text{ } \Omega. Find RTR_T.

Example 3

hard
Three identical bulbs in parallel pull a total of 6 A6 \text{ A} from a 120 V120 \text{ V} source. Find each bulb's resistance.

Example 4

easy
In a parallel circuit, do the branch currents add to the total current?

Example 5

medium
Two resistors in parallel give a total of 4 Ω4 \text{ } \Omega. If one resistor is 6 Ω6 \text{ } \Omega, find the other.

Example 6

hard
Two resistors are connected first in series, giving Rs=25 ΩR_s = 25 \text{ } \Omega, then in parallel, giving Rp=4 ΩR_p = 4 \text{ } \Omega. Find the two resistances.

Example 7

challenge
nn identical RR-ohm resistors are connected in parallel. By what factor does the power dissipated by the network change as nn goes from 1 to 4, with the same source voltage VV?

Example 8

hard
When a 4 Ω4 \text{ } \Omega resistor is added in parallel to an existing 8 Ω8 \text{ } \Omega resistor, by what factor does the total resistance change?

Example 9

challenge
Three parallel branches across 2424 V carry 22 A, 33 A, and 11 A. Find the equivalent resistance of the combination.

Example 10

hard
A 10 V10 \text{ V} battery drives two parallel branches: branch 1 is two 4 Ω4 \text{ } \Omega resistors in series, branch 2 is one 2 Ω2 \text{ } \Omega resistor. Find the total current.

Example 11

medium
Two parallel resistors 2 Ω2\,\Omega and 2 Ω2\,\Omega connect across 88 V. Find the total current.

Example 12

medium
A 1212 V source feeds 3 Ω3\,\Omega and 6 Ω6\,\Omega in parallel. Find each branch current.

Example 13

medium
A 20 Ω20\,\Omega and a 5 Ω5\,\Omega resistor are in parallel. Use product-over-sum to find the total resistance.

Example 14

easy
A 1212 V source feeds two parallel branches. What voltage is across each branch?

Example 15

easy
A 12 V12 \text{ V} battery is connected to a single 6 Ω6 \text{ } \Omega branch and a 3 Ω3 \text{ } \Omega branch in parallel. What is the current in the 3 Ω3 \text{ } \Omega branch?

Example 16

medium
A 20 Ω20 \text{ } \Omega resistor and a 30 Ω30 \text{ } \Omega resistor are in parallel. Find RTR_T.

Example 17

medium
A toaster (15 Ω15 \text{ } \Omega), a lamp (60 Ω60 \text{ } \Omega), and a heater (10 Ω10 \text{ } \Omega) are in parallel across 120 V120 \text{ V}. Find the total power.

Example 18

medium
Two parallel branches carry 2 A2 \text{ A} and 3 A3 \text{ A}. What is the supply current?

Example 19

medium
A 24 V24 \text{ V} battery is connected to three parallel resistors: 6 Ω6 \text{ } \Omega, 8 Ω8 \text{ } \Omega, and 12 Ω12 \text{ } \Omega. Find the total current drawn from the battery.

Example 20

easy
Is the total resistance of a parallel combination larger or smaller than the smallest branch?
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