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

A cell with an electromotive force (e.m.f.) of $12.0\text{ V}$ and an internal resistance of $1.5\ \Omega$ is connected in series to an external resistor of $8.5\ \Omega$ . What is the terminal potential difference across the cell?

Answer: 10.2 V

Answer

The terminal potential difference across the cell is

10.2\text{ V}

The terminal potential difference

V

across a real cell supplying current is less than its electromotive force

E

due to the internal voltage drop

Ir

. By first determining the circuit current

I = \frac{E}{R + r} = \frac{12.0}{8.5 + 1.5} = 1.2\text{ A}

, the terminal potential difference is calculated as

V = I \times R = 1.2 \times 8.5 = 10.2\text{ V}

(or equivalently

V = E - I r = 12.0 - (1.2 \times 1.5) = 10.2\text{ V}

Step-by-Step Solution

Calculate the total resistance of the circuit

R_{\text{total}} = 10.0\ \Omega

The external load resistor and the cell's internal resistance are in series.

Determine the total current drawn from the cell

I = 1.2\text{ A}

Using Ohm's law applied to the entire circuit,

I = \frac{E}{R + r}

Calculate the potential drop across the external load resistor

V = 10.2\text{ V}

Terminal voltage equals potential difference across external load (

V = I R

) or

V = E - I r

Key Concept

Terminal Potential Difference and Internal Resistance

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