First slide

Phasors and Phasor Diagrams

Question

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 AC source of 110 V. The power factor of the circuit is

Moderate

A

0.56
B

0.64
C

0.80
D

0.33

Solution

power factor $(cosϕ)$ is a ratio of resistance and impedance of AC circuit.
Power factor of AC circuit is given by
$cosϕ = \frac{R}{Z}$ …(i)
$Z = \sqrt{R^{2} + (X_{L} - X_{C}^{2})}$ ….(ii)
Equations (i) and (ii) give,
$cosϕ = \frac{R}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}}$ …(iii)
Given, $R = 8 Ω, X_{L} = 31 Ω, X_{C} = 25 Ω$
$cosϕ = \frac{8}{\sqrt{(8)^{2} + (31 - 25)^{2}}} = \frac{8}{\sqrt{64 + 36}}$
$cosϕ = 0 .80$

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