When switch S in Fig. 𝐄 25.29 is open, the voltmeter V reads 3.14 V. When the switch is closed,

step 1 The volt meter reads the potential difference VAB between the terminals of the battery. So VAB e

When switch S in Fig. 𝐄 25.29 is open, the voltmeter V reads...

When switch $S$ in Fig. $\mathbf{E} 25.29$ is open, the voltmeter $\mathrm{V}$ reads $3.14 \mathrm{~V}$. When the switch is closed, the voltmeter reading drops to $2.93 \mathrm{~V}$, and the ammeter A reads 1.67 A. Find the emf, the internal resistance of the battery, and the circuit resistance $R$. Assume that the two meters are ideal, so they don't affect the circuit.

Key Concepts

Open-Circuit vs Loaded Measurements

Open-circuit voltage measurements are taken when no external current is drawn from the battery, providing a value that is nearly equal to the emf of the battery. In contrast, when the circuit is loaded, the measured voltage (terminal voltage) drops due to the internal resistance of the battery, and this difference can be used to analyze the circuit parameters.

Ohm's Law

Ohm's Law states that the voltage across a resistor is directly proportional to the current flowing through it, with the resistance being the constant of proportionality. This fundamental principle is used to relate the measured voltage and current in a circuit and to calculate unknown resistances when either the voltage drop or current is known.

Series Circuit Analysis

In a series circuit, all components are connected end?to?end so that the same current flows through each element. The total voltage supplied by the battery is divided among the series elements, such as the battery’s internal resistance and the external circuit resistance, according to their individual resistances.

Internal Resistance of a Battery

Every battery has an inherent internal resistance that causes a voltage drop when current is drawn. This means that the terminal voltage of a battery under load is lower than its electromotive force (emf). Measuring the drop between the open-circuit voltage (which approximates the emf) and the loaded voltage allows one to determine the internal resistance.

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