Terminal Voltage Calculation for Battery with Resistors

Chapter 26, Problem 1

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QUESTION:

Calculate the terminal voltage for a battery with an internal resistance of \(0.900 \Omega\) and an emf of \(6.00 V\) when the battery is connected in series with (a) an \(81.0-\Omega\) resistor, and(ib) an \(810-\Omega\) resistor.

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Terminal Voltage Calculation for Battery with Resistors
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Unlock the secrets of battery performance in this video! We calculate the terminal voltage for a battery with internal resistance, connected in series with resistors of different values. Explore the effects of resistance on voltage in electrical circuits.

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Questions & Answers

QUESTION:

Calculate the terminal voltage for a battery with an internal resistance of \(0.900 \Omega\) and an emf of \(6.00 V\) when the battery is connected in series with (a) an \(81.0-\Omega\) resistor, and(ib) an \(810-\Omega\) resistor.

ANSWER:

 

Step 1 of 2:

(a)

Given:

Internal resistance: \(r=0.9 \Omega\)

\(\text { Emf: }=6 \mathrm{~V}\)

Resistance: \(R=81 \Omega\)

Total Resistance: \(R_{t}=R+r=81+0.9=81.9 \Omega\)

Current Flowing through the circuit: \(I=\frac{6}{81.9}=0.073 \mathrm{~A}\)

Terminal Voltage

\(\begin{array}{l} V=-I r \\ V=6-0.073(0.9) \\ V=6-0.0657=5.93 \mathrm{~V} \end{array}\)

Hence the terminal voltage is \(5.93V\)

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