A battery with an electromotive force (e.m.f.) of 12.0\text{ V} and an internal resistance… — JAMB UTME

A battery with an electromotive force (e.m.f.) of $12.0\text{ V}$ and an internal resistance of $1.0\text{ }\Omega$ is connected across a load resistor of $5.0\text{ }\Omega$ . What is the terminal potential difference across the battery in volts?

Answer: 10 V

Answer

The terminal potential difference across the battery is

10.0\text{ V}

The total resistance in the circuit is the sum of the external load resistance and the battery's internal resistance (

R_{\text{total}} = 5.0\text{ }\Omega + 1.0\text{ }\Omega = 6.0\text{ }\Omega

). The current drawn from the battery is

I = \frac{12.0\text{ V}}{6.0\text{ }\Omega} = 2.0\text{ A}

. The terminal potential difference available to the external load is

V = I \cdot R = 2.0\text{ A} \times 5.0\text{ }\Omega = 10.0\text{ V}

Step-by-Step Solution

Find the total circuit resistance including internal resistance

R_{\text{total}} = 5.0\text{ }\Omega + 1.0\text{ }\Omega = 6.0\text{ }\Omega

The internal resistance of the cell acts in series with the external load resistor.

Determine total current in the circuit

I = \frac{E}{R_{\text{total}}} = \frac{12.0\text{ V}}{6.0\text{ }\Omega} = 2.0\text{ A}

By Ohm's law, current equals total electromotive force divided by total circuit resistance.

Compute the terminal potential difference

V = I \times R = 2.0\text{ A} \times 5.0\text{ }\Omega = 10.0\text{ V}

Terminal voltage is the voltage drop across the load resistor, equivalent to

E - I \cdot r

Key Concept

Terminal Potential Difference and Internal Resistance

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