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WAEC Physics 2012 Paper

Question : 41

Total: 47

π = \frac{22}{7}

)

Solution:

Concept:

An inductor in an AC circuit opposes the current with inductive reactance

X_L

, defined by

X_L = \frac{V}{I}

The inductance is then found from the relation

X_L = 2\pi f L

Explanation:

First, find the inductive reactance using the supply voltage and current.

X_L = \frac{V}{I} = \frac{24}{1.5} = 16\,\Omega

Now use

X_L = 2\pi f L

and rearrange to get

L = \frac{X_L}{2\pi f}

Substitute

X_L = 16\,\Omega

and

f = 50\,\mathrm{Hz}

L = \frac{16}{2\pi \times 50}

Since

\pi = \frac{22}{7}

L = \frac{16}{100 \times \frac{22}{7}} = \frac{16 \times 7}{2200} = \frac{112}{2200} \approx 0.0509\,\mathrm{H}

This is equivalent to

5.1 \times 10^{-2}\,\mathrm{H}

Answer:

L = 5.1 \times 10^{-2}\,\mathrm{H}

, which is option D.

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