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Problem 10: A coil having a resistance of 7 Ω and inductance of 31.8 mH is connected to 230 V, 50 Hz supply. Calculate (a) the circuit current (b) Phase angle (c) Power factor (d) Power consumed.

Solution

Given:
R = 7 Ω,
L = 31.8 mH = 31.8 × 10-3 H
V = 230 V
f = 50 Hz

Required: I, ϕ, cosϕ, P

(a) Since I = V/Z, where Z is the impedance of the circuit and given by

Now

Put in the above formula,

Now put this value of Z in the equation for the current, I = 230/12.2 = 18.85 Amp

(b) Phase angle
(lagging behind)

(c) Power factor is given by cosϕ

(d) Power consumed = VIcosϕ =230 × 18.85 × 0.573 = 2484.2 Watt

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