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JAMB Physics 2024 Paper

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Question : 39

Total: 125

A cell of internal resistance of 2

\Omega

supplies current through a resistor, X if the efficiency of the cell is 75%, find the value of X.

2 $\Omega$
4 $\Omega$
6 $\Omega$
8 $\Omega$

Solution:

Concept:

The efficiency of a cell depends on the external resistance

X

and the internal resistance

r

.

It is given by:

\text{efficiency} = \dfrac{X}{X + r} \times 100\%

.

Explanation:

Internal resistance,

r = 2\ \Omega

.

External resistance,

X

is unknown.

Efficiency

= 75\% = 0.75

.

Substitute into the formula:

0.75 = \frac{X}{X + 2}

Multiply both sides by

X + 2

:

0.75(X + 2) = X

0.75X + 1.5 = X

Rearrange to collect like terms:

1.5 = X - 0.75X

1.5 = 0.25X

Divide both sides by

0.25

:

X = \frac{1.5}{0.25} = 6\ \Omega

Answer:

The value of

X

is

6\ \Omega

.

Correct option: C.

6\ \Omega

.

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