Parallel Circuit Examples in Physics

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

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept 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.

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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: Parallel Circuit 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 parallel circuit 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?

Worked Examples

Example 1

medium

Two resistors (

6 \text{ } \Omega

and

12 \text{ } \Omega

) are connected in parallel to a

12 \text{ V}

battery. What is the total resistance and the current through each resistor?

Answer

R_T = 4 \text{ } \Omega; \quad I_1 = 2 \text{ A}, I_2 = 1 \text{ A}

First step

Total resistance:

\frac{1}{R_T} = \frac{1}{6} + \frac{1}{12} = \frac{2}{12} + \frac{1}{12} = \frac{3}{12} \implies R_T = 4 \text{ } \Omega

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Example 2

hard

Three identical

30 \text{ } \Omega

resistors are connected in parallel. What is the total resistance?

Example 3

medium

Three resistors of

6 \text{ } \Omega

12 \text{ } \Omega

, and

4 \text{ } \Omega

are connected in parallel. Find the total resistance.

Example 4

medium

24 \text{ V}

battery is connected to three parallel resistors:

6 \text{ } \Omega

8 \text{ } \Omega

, and

12 \text{ } \Omega

. Find the total current drawn from the battery.

Example 5

medium

Four identical bulbs of

60 \text{ } \Omega

each are in parallel across a

120 \text{ V}

source. Find the total current.

Example 6

medium

A toaster (

15 \text{ } \Omega

), a lamp (

60 \text{ } \Omega

), and a heater (

10 \text{ } \Omega

) are in parallel across

120 \text{ V}

. Find the total power.

Example 7

hard

A battery of EMF

12 \text{ V}

and internal resistance

1 \text{ } \Omega

drives two parallel resistors

4 \text{ } \Omega

and

6 \text{ } \Omega

. Find the current drawn from the battery.

Example 8

hard

10 \text{ V}

battery drives two parallel branches: branch 1 is two

4 \text{ } \Omega

resistors in series, branch 2 is one

2 \text{ } \Omega

resistor. Find the total current.

Example 9

challenge

n

identical

R

-ohm resistors are connected in parallel. By what factor does the power dissipated by the network change as

n

goes from 1 to 4, with the same source voltage

V

Practice Problems

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

Example 1

medium

10 \text{ } \Omega

and a

15 \text{ } \Omega

resistor are in parallel. What is the combined resistance?

Example 2

medium

Two resistors (

10 \text{ } \Omega

and

15 \text{ } \Omega

) are connected in parallel across a

30 \text{ V}

supply. Find: (a) total resistance, (b) total current, (c) current through each resistor.

Example 3

easy

How do you find the total resistance of resistors in parallel?

Example 4

easy

In a parallel circuit, is the voltage the same across each branch?

Example 5

easy

Two

4\,\Omega

resistors are in parallel. What is the total resistance?

Example 6

easy

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

Example 7

easy

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

Example 8

easy

If one branch of a parallel circuit is removed, do the other branches still carry current?

Example 9

easy

12

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

Example 10

easy

Three

6\,\Omega

resistors are in parallel. What is the total resistance?

Example 11

medium

6\,\Omega

and a

12\,\Omega

resistor are in parallel. Find the total resistance.

Example 12

medium

12

V source feeds

4\,\Omega

and

6\,\Omega

in parallel. Find the current in each branch.

Example 13

medium

In the previous setup (

4\,\Omega

and

6\,\Omega

across

12

V), find the total current from the source.

Example 14

medium

Two parallel resistors

10\,\Omega

and

15\,\Omega

connect to a source drawing

1

A total. Find the source voltage.

Example 15

medium

20\,\Omega

and a

5\,\Omega

resistor are in parallel. Use product-over-sum to find the total resistance.

Example 16

medium

A parallel pair

3\,\Omega

and

6\,\Omega

across

12

V dissipates how much total power?

Example 17

medium

A parallel circuit has total current

9

A. One branch carries

4

A. If there are only two branches, what does the other carry?

Example 18

challenge

4\,\Omega

resistor is in parallel with a series combination of

2\,\Omega

and

4\,\Omega

. Find the total resistance.

Example 19

challenge

Three parallel branches across

24

V carry

2

3

A, and

1

A. Find the equivalent resistance of the combination.

Example 20

challenge

A current of

12

A enters a parallel combination of

3\,\Omega

and

6\,\Omega

. Use the current-divider idea to find each branch current.

Example 21

medium

12

V source feeds

3\,\Omega

and

6\,\Omega

in parallel. Find each branch current.

Example 22

medium

Two parallel resistors

2\,\Omega

and

2\,\Omega

connect across

8

V. Find the total current.

Example 23

easy

Two

8 \text{ } \Omega

resistors are in parallel. Find the total resistance.

Example 24

easy

12 \text{ V}

battery is connected to a single

6 \text{ } \Omega

branch and a

3 \text{ } \Omega

branch in parallel. What is the current in the

3 \text{ } \Omega

branch?

Example 25

easy

Three

9 \text{ } \Omega

resistors are in parallel. Find the total resistance.

Example 26

medium

20 \text{ } \Omega

resistor and a

30 \text{ } \Omega

resistor are in parallel. Find

R_T

Example 27

medium

12 \text{ V}

battery feeds a

4 \text{ } \Omega

and a

6 \text{ } \Omega

resistor in parallel. Find the power dissipated in the

4 \text{ } \Omega

resistor.

Example 28

medium

Two resistors in parallel give a total of

4 \text{ } \Omega

. If one resistor is

6 \text{ } \Omega

, find the other.

Example 29

medium

9 \text{ V}

battery is across three parallel resistors of

3 \text{ } \Omega

6 \text{ } \Omega

, and

9 \text{ } \Omega

. Find

R_T

Example 30

medium

Two parallel branches carry

2 \text{ A}

and

3 \text{ A}

. What is the supply current?

Example 31

medium

Two parallel resistors

R_1

and

R_2

. If

R_1 = R_2

, what is

R_T/R_1

Example 32

medium

Three resistors in parallel give a total of

2 \text{ } \Omega

. Two are

6 \text{ } \Omega

and

12 \text{ } \Omega

. Find the third.

Example 33

hard

30 \text{ V}

source drives a

5 \text{ } \Omega

and a

15 \text{ } \Omega

resistor in parallel. Find the ratio of power dissipated in the

5 \text{ } \Omega

to that in the

15 \text{ } \Omega

Example 34

hard

Two resistors are connected first in series, giving

R_s = 25 \text{ } \Omega

, then in parallel, giving

R_p = 4 \text{ } \Omega

. Find the two resistances.

Example 35

hard

Three identical bulbs in parallel pull a total of

6 \text{ A}

from a

120 \text{ V}

source. Find each bulb's resistance.

Example 36

hard

When a

4 \text{ } \Omega

resistor is added in parallel to an existing

8 \text{ } \Omega

resistor, by what factor does the total resistance change?

Example 37

hard

50 \text{ } \Omega

and a

200 \text{ } \Omega

resistor are in parallel. What is the equivalent resistance?

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Related Concepts

Circuit Resistance Ohm's Law Circuit Diagram Kirchhoff's Laws Electrical Power

Background Knowledge

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

circuitresistanceohms law