The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L-C-R circuit. The power factor of this circuit is [2016]

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Solution

Q.
The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L-C-R circuit. The power factor of this circuit is [2016]

1 0.4

2 0.5

3 0.8

4 1.0

Ans.
(3)

Here, $V_{R} = 80$ $V,$ $V_{C} = 40$ $V,$ $V_{L} = 100$ $V$

Power factor, $\cos ϕ = \frac{R}{Z} = \frac{V_{R}}{V} = \frac{V_{R}}{\sqrt{V_{R}^{2} + {(V_{L} - V_{C})}^{2}}}$

$= \frac{80}{\sqrt{{(80)}^{2} + {(100 - 40)}^{2}}} = \frac{80}{100} = 0.8$

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