Question

A battery of emf 21 V and internal resistance 3 $\Omega$ is connected to a resistor. If the current in the circuit is 3 A, find the terminal voltage of the battery.

Hint:

Always cross-verify your answer in exam scenarios. If $E - Ir$ matches $I \times R$, you can be 100% confident your calculated resistance and terminal voltage are correct.

Answer 1

Concept:
• The terminal voltage ($V$) is the actual potential difference available across the terminals of the battery when a current is drawn from it.
• Due to the voltage drop across the internal resistance, the terminal voltage is always less than the emf when the battery is discharging.
• It can be calculated using $V = E - Ir$ or by calculating the voltage drop across the external resistor $V = IR$.

Step 1: Identify given values
Electromotive force, $E = 21 \text{ V}$. Internal resistance, $r = 3\ \Omega$. Current in the circuit, $I = 3 \text{ A}$. External resistance calculated previously, $R = 4\ \Omega$.

Step 2: Calculate the terminal voltage using the battery parameters
The formula for terminal voltage during discharge is: \[ V = E - I \cdot r \]
Substitute the values: \[ V = 21 - (3 \times 3) \]
\[ V = 21 - 9 \]
\[ V = 12 \text{ V} \]

Step 3: Alternative calculation using external resistance
The terminal voltage is also equal to the potential drop entirely across the external circuit: \[ V = I \cdot R \]
Substitute the values: \[ V = 3 \times 4 \]
\[ V = 12 \text{ V} \]
Both methods yield the exact same result.

Step 4: Conclusion
The terminal voltage of the battery is $12 \text{ V}$.