---
title: Circuit with Multiple Voltage Sources
topic: Circuits
author: Joseph Wandinger
source: 2.10.36
template_version: 1.3
attribution: openstax-physics-vol2
partialCredit: true
singleVariant: false
showCorrectAnswer: false
outcomes:
- 21.8.1.1
- 21.8.2.0
- 21.12.1.0
difficulty:
- undefined
randomization:
- undefined
taxonomy:
- undefined
span:
- undefined
length:
- undefined
tags:
- OSUP
- volume 2
- chapter 10
- problem 36
- circuits
- electrical power
- multi-part
- JW
assets:
- fig_OSUPv2p10_36.png
part1:
  type: number-input
  pl-customizations:
    label: $V_{R_1} = $
    allow-blank: false
    show-correct-answer: false
    comparison: relabs
    rtol: 0.03
    atol: 0
    show-help-text: true
    suffix: $\rm\ V$
    weight: 1
    custom-format: .3g
part2:
  type: number-input
  pl-customizations:
    label: $V_{R_2} = $
    allow-blank: false
    show-correct-answer: false
    comparison: relabs
    rtol: 0.03
    atol: 0
    show-help-text: true
    suffix: $\rm\ V$
    weight: 1
    custom-format: .3g
part3:
  type: number-input
  pl-customizations:
    label: $V_{R_3} = $
    allow-blank: false
    show-correct-answer: false
    comparison: relabs
    rtol: 0.03
    atol: 0
    show-help-text: true
    suffix: $\rm\ V$
    weight: 1
    custom-format: .3g
part4:
  type: number-input
  pl-customizations:
    label: $V_{R_4} = $
    allow-blank: false
    show-correct-answer: false
    comparison: relabs
    rtol: 0.03
    atol: 0
    show-help-text: true
    suffix: $\rm\ V$
    weight: 1
    custom-format: .3g
part5:
  type: number-input
  pl-customizations:
    label: $V_{R_5} = $
    allow-blank: false
    show-correct-answer: false
    comparison: relabs
    rtol: 0.03
    atol: 0
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    suffix: $\rm\ V$
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part6:
  type: number-input
  pl-customizations:
    label: $P_{\rm\ in} = $
    allow-blank: false
    show-correct-answer: false
    comparison: relabs
    rtol: 0.03
    atol: 0
    show-help-text: true
    suffix: $\rm\ W$
    weight: 1
    custom-format: .3g
part7:
  type: number-input
  pl-customizations:
    label: $P_{\rm\ out} = $
    allow-blank: false
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    rtol: 0.03
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    suffix: $\rm\ W$
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myst:
  substitutions:
    params:
      vars:
        title: Circuit with Multiple Voltage Sources
      R1: '12.0'
      R2: '21.0'
      R3: '15.0'
      R4: '18.0'
      R5: '20.0'
      V1: '15.0'
      V2: '20.5'
---
# {{ params.vars.title }}
Consider the circuit shown below.

<img src="fig_OSUPv2p10_36.png" width=250>

The battery voltages are $V_1 = {{ params.V1 }}\rm\ V$ and $V_2 = {{ params.V2 }}\rm\ V$.
The resistances are $R_1 = {{ params.R1 }}\rm\ k \Omega$, $R_2 = {{ params.R2 }}\rm\ k \Omega$, $R_3 = {{ params.R3 }}\rm\ k \Omega$, $R_4 = {{ params.R4 }}\rm\ k \Omega$, and $R_5 = {{ params.R5 }}\rm\ k \Omega$.

## Part 1

What is the voltage across $R_1$?

### Answer Section

Please enter in a numeric value in $\rm\ V$.

## Part 2

What is the voltage across $R_2$?

### Answer Section

Please enter in a numeric value in $\rm\ V$.

## Part 3

What is the voltage across $R_3$?

### Answer Section

Please enter in a numeric value in $\rm\ V$.

## Part 4

What is the voltage across $R_4$?

### Answer Section

Please enter in a numeric value in $\rm\ V$.

## Part 5

What is the voltage across $R_5$?

### Answer Section

Please enter in a numeric value in $\rm\ V$.

## Part 6

What is the power supplied to the circuit?

### Answer Section

Please enter in a numeric value in $\rm\ W$.

## Part 7

What is the power dissipated by the circuit?

### Answer Section

Please enter in a numeric value in $\rm\ W$.

## Attribution

Problem is from the [OpenStax University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2) textbook, licensed under the [CC-BY 4.0 license](https://creativecommons.org/licenses/by/4.0/).<br>![Image representing the Creative Commons 4.0 BY license.](https://raw.githubusercontent.com/firasm/bits/master/by.png)