Question

A resistor is connected to a battery of 12 V emf and internal resistance 2 $\Omega$. If the current in the circuit is 0.6 A, the terminal voltage of the battery is: ____.

• A. 10.8 V
• B. 1.2 V
• C. 12 V
• D. 10 V

Hint:

Terminal voltage $V$ is equal to $E$ only when no current is flowing (open circuit). As soon as current flows, the battery "wastes" some energy internally.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Terminal voltage ($V$) is the potential difference across the terminals of a battery when current is flowing. It is always less than the electromotive force (emf) due to the voltage drop across the internal resistance ($r$).

Step 2: Key Formula or Approach:
\[ V = E - Ir \] Where: - $E$ is the emf of the battery. - $I$ is the current. - $r$ is the internal resistance.

Step 3: Detailed Explanation:
Given: $E = 12$ V, $r = 2\,\Omega$, $I = 0.6$ A. 1. Calculate the voltage drop across the internal resistance ($v_{drop}$): \[ v_{drop} = I \times r = 0.6 \times 2 = 1.2 \text{ V} \] 2. Subtract this drop from the emf to find the terminal voltage: \[ V = 12 - 1.2 = 10.8 \text{ V} \]

Step 4: Final Answer:
The terminal voltage of the battery is 10.8 V.