A cell of electromotive force (e.m.f.) 1.5\text{ V} and internal resistance 0.5\text{ }\Om… — JAMB UTME

A cell of electromotive force (e.m.f.) $1.5\text{ V}$ and internal resistance $0.5\text{ }\Omega$ is connected in series with a $2.5\text{ }\Omega$ resistor. What is the terminal potential difference across the cell?

$1.25\text{ V}$ Answer
B
$1.50\text{ V}$
C
$0.25\text{ V}$
D
$1.75\text{ V}$

Answer

The terminal potential difference across the cell is

1.25\text{ V}

When current flows through a closed circuit, voltage drops across both the external load resistor and the cell's internal resistance. Subtracting the lost voltage (

0.25\text{ V}

) from the electromotive force (

1.50\text{ V}

) yields a terminal potential difference of

1.25\text{ V}

Step-by-Step Solution

Calculate the total resistance of the circuit

R_{\text{total}} = R + r = 2.5\text{ }\Omega + 0.5\text{ }\Omega = 3.0\text{ }\Omega

The external load resistor and the internal resistance of the cell are connected in series.

Calculate the total electric current flowing through the circuit

I = \frac{E}{R + r} = \frac{1.5\text{ V}}{3.0\text{ }\Omega} = 0.5\text{ A}

Ohm's law for a complete circuit states that current equals total e.m.f. divided by total circuit resistance.

Determine the terminal potential difference across the cell

V = I \times R = 0.5\text{ A} \times 2.5\text{ }\Omega = 1.25\text{ V}

Terminal potential difference is the potential drop across the external resistance.

Key Concept

Terminal Potential Difference and Cell Internal Resistance

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