A DC supply with an electromotive force (e.m.f.) of 24.0\text{ V} and an internal resistan… — JAMB UTME

A DC supply with an electromotive force (e.m.f.) of $24.0\text{ V}$ and an internal resistance of $2.0\text{ }\Omega$ is connected across three identical $12.0\text{ }\Omega$ resistors connected in parallel. What is the terminal potential difference across the battery in volts?

Answer: 16 V

Answer

The terminal potential difference across the battery is

16.0\text{ V}

The three identical

12.0\text{ }\Omega

resistors in parallel combine to yield an equivalent external resistance of

4.0\text{ }\Omega

. Adding the battery's internal resistance of

2.0\text{ }\Omega

gives a total circuit resistance of

6.0\text{ }\Omega

. The total current drawn from the battery is

I = \frac{24.0\text{ V}}{6.0\text{ }\Omega} = 4.0\text{ A}

. The terminal potential difference is the voltage drop across the external circuit,

V = 4.0\text{ A} \times 4.0\text{ }\Omega = 16.0\text{ V}

Step-by-Step Solution

Find the equivalent external resistance of the three parallel resistors.

R_p = 4.0\text{ }\Omega

Three identical resistors

R = 12.0\text{ }\Omega

connected in parallel have an equivalent resistance of

R_p = \frac{12.0}{3} = 4.0\text{ }\Omega

Find the total circuit resistance by adding internal resistance to the parallel combination.

R_{total} = 6.0\text{ }\Omega

Internal resistance

r = 2.0\text{ }\Omega

acts in series with the external parallel combination:

R_{total} = R_p + r = 4.0 + 2.0 = 6.0\text{ }\Omega

Calculate the total current supplied by the cell.

I = 4.0\text{ A}

Using the circuit formula

I = \frac{E}{R_{total}}

, we divide the e.m.f. of

24.0\text{ V}

by the total resistance of

6.0\text{ }\Omega

Compute the terminal potential difference across the cell.

V = 16.0\text{ V}

The potential drop across the external parallel network is

V = I R_p = 4.0\text{ A} \times 4.0\text{ }\Omega = 16.0\text{ V}

, which equals

E - Ir = 24.0\text{ V} - (4.0\text{ A} \times 2.0\text{ }\Omega) = 16.0\text{ V}

Key Concept

Terminal Potential Difference and Internal Resistance

Estimated Time:1m 30s

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