The diagram below illustrates an a.c.source of 50V(r.m.s.), \(\frac{100}{\pi}\)Hz connected in series with an inductor...

WAEC 1998

The diagram below illustrates an a.c.source of 50V(r.m.s.), \(\frac{100}{\pi}\)Hz connected in series with an inductor of inductor of inductance L and a resistor of resistance R. The current in the circuit is 2A and the p.d across L and R are 30V and 40V respectively. Calculate the power factor of the circuit

A. 1.33
B. 1.25
C. 0.80
D. 0.75
E. 0.60

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Correct Answer: Option C

Explanation

cos\(\theta = \frac{R}{Z}\)

R = \(\frac{V}{I} = \frac{40}{2} = 20\)

Z² = R² + \(^X_L\)² = 20² + 15² = √625 = 25

cos \(\theta = \frac{R}{Z} = \frac{20}{25} = 0.8\)

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