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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 measure the voltage of a battery, connect the voltmeter across the battery terminals in an open circuit. The voltage measured will be the battery's total voltage or EMF. Then connect a resistance across the battery terminals and measure the terminal voltage and current. The internal resistance of the battery can be calculated using these measurements through the re-arranged form of Ohm's law \(r = \frac{E - V_t}{I}\) where \(E\) is the EMF, \(V_t\) is the terminal voltage, \(I\) is the current, and \(r\) is the internal resistance.

Step by step solution

01

Measure the open-circuit voltage

Connect the voltmeter across the terminals of the battery with no other components in the circuit. This is known as an open circuit condition. The voltmeter reading will give the total voltage (or EMF, Electromotive force) of the battery, as no current is flowing in this case due to the infinite resistance of the voltmeter. Let's denote this value as \(E\).
02

Measure the closed-circuit voltage and current

Introduce a resistance across the battery terminals and measure both the terminal voltage and the current flowing in the circuit using the voltmeter and the ammeter respectively. Now, the voltage across the battery terminals will be slightly lower due to the internal resistance of the battery itself, and this voltage is usually referred to as the terminal voltage of the battery. Let's denote this voltage as \(V_t\) and the current as \(I\).
03

Calculate internal resistance

The voltage drop causing the difference between the open-circuit voltage (EMF) and closed-circuit terminal voltage is due to the current flowing through the internal resistance of the battery as per Ohm's Law. We can find the internal resistance \(r\) using this fact and the values obtained from the previous steps by arranging Ohm's Law like so: \(r = \frac{E - V_t}{I}\).

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Most popular questions from this chapter

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