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Chapter 25: Problem 10

You have a battery whose voltage and internal resistance are unknown. Using an ideal voltmeter and an ideal ammeter, how would you determine each of these characteristics?

Short Answer

Expert verified
To determine the battery's internal resistance, measure the open-circuit voltage using a voltmeter, then connect a known resistor in series and measure the current with an ammeter. The internal resistance is calculated using Ohm's law as \( r = \frac{V - V_{t}}{I}\) where \(V\) is the open-circuit voltage, \(V_{t}\) is the terminal voltage under load, and \(I\) is the current. The voltage of the battery is the measured open-circuit voltage

Step by step solution

01

Understand the Task

The aim is to figure out the voltage and internal resistance of a battery using an ideal voltmeter and an ideal ammeter. The voltmeter measures the voltage accross the terminals of the battery when there is no external resistance connected (short circuit), and the ammeter measures the current through the battery.
02

Measure the Open-Circuit Voltage

Connect the voltmeter across the battery, without anything else connected. This is known as a no-load condition. The voltmeter now indicates the open-circuit voltage \(V\), which is also the emf of the cell.
03

Measure the Battery Current

Next, add a resistor before connecting the ammeter in series with the battery. Measure the current (I) flowing through the circuit.
04

Measure the Terminal Voltage

Then measure the terminal voltage (\(V_{t}\)) across the battery using the voltmeter connected in parallel while current is flowing. This voltage will be less than the open-circuit voltage due to internal resistance (\(r\)) of the battery consuming some of the energy.
05

Calculate the Internal Resistance

By using Ohm's Law, and knowing that the lost potential difference is \( V - V_{t} = I \cdot r\), re-arrange this equation to solve for \(r\) : \( r = \frac{V - V_{t}}{I}\). Substitute the measured values in this equation to calculate the internal resistance.

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Most popular questions from this chapter

Can the voltage across a battery's terminals be higher than the battery's rated voltage? Explain.

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Sketch a circuit diagram for a circuit that includes a resistor \(R_{\square}\) connected to the positive terminal of a battery, a pair of paralle resistors \(R_{2}\) and \(R_{3}\) connected to the lower-voltage end of \(R_{1}\) and then returned to the battery's negative terminal, and a capacitor across \(R_{2}\)
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