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 Topic:
This problem is part of "Current Electricity," focusing on the behavior of real voltage sources. Unlike an ideal battery, a real battery has internal resistance which causes a voltage drop inside the battery itself when current is drawn from it.
Step 2: Key Formulas and Approach:
The terminal voltage ($V$) is the potential difference measured across the battery's terminals when it is part of a closed circuit. \[ V = E - Ir \] Where:
$E$ = Electromotive force (emf) of the battery (voltage when $I=0$).
$I$ = Current flowing through the circuit.
$r$ = Internal resistance of the battery.

Step 3: Detailed Explanation:

Identify given values: Emf $E = 12 \text{ V}$, Internal resistance $r = 2 \Omega$, and Current $I = 0.6 \text{ A}$.
Calculate the internal voltage drop: When current flows through the internal resistance, some of the battery's energy is dissipated as heat. This "lost voltage" is calculated using Ohm's Law: \[ V_{internal} = I \times r = 0.6 \text{ A} \times 2 \Omega = 1.2 \text{ V} \]
Determine Terminal Voltage: The voltage available to the rest of the circuit is the total emf minus this internal drop: \[ V = 12 \text{ V} - 1.2 \text{ V} = 10.8 \text{ V} \]
This means the external resistor connected to this battery will only receive 10.8 V, not the full 12 V.
Step 4: Final Answer:
The terminal voltage of the battery is 10.8 V.