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Q.

A circuit shown in the figure contains a box having either a capacitor or an inductor. The power factor of the circuit is 0.8, while current lags behind the voltage. Then find the inductance/capacitance of the box in S.I. unit. (Take $π = 3.2$ ) The circuit draws 1 ampere current.

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answer is 2.5.

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Detailed Solution

$X_{c} = \frac{V_{c}}{1} = \frac{1000}{1} = 1000 Ω$
Current lags behind voltage
So, box has an inductor
Power factor $= 0.8 = \frac{R}{Z} = \frac{800}{\sqrt{{(800)}^{2} + {(X_{L} - 1000)}^{2}}}$
$X_{L} = 1600 Ω ω L = 1600 L = \frac{1600}{2 \times 3.2 \times 100} = 2.5 H$

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