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A coil of inductive reactance $31 Ω$ has a resistance of $8 Ω .$ It is placed in series with a condenser of capacitive reactance $25 Ω .$ The combination is connected to an a source of 110V. The power factor of the circuit is

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0.80

0.33

0.56

0.64

answer is C.

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Detailed Solution

$X_{L} = 31 Ω$ $R = 8 Ω$ $X_{C} = 25 Ω$

$V = 100 V$

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}$

$Z = \sqrt{8^{2} + {(31 - 25)}^{2}}$

$Z = \sqrt{8^{2} + {(6)}^{2}} = \sqrt{64 + 36}$

$Z = \sqrt{100} = 10$

$\cos ϕ = \frac{R}{Z}$

$\cos ϕ = \frac{8}{10} = 0.8$

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