Question

A voltage v (t) = 141.4 sin (314 t + 10°) is applied to a circuit and the steady current given by i(t) = 14.14 sin (314 t − 20°) is found to flow through it.Determine

(i) The p.f. of the circuit

(ii) The power delivered to the circuit

(iii) Draw the phasor diagram.

Answer 1

v(t) = 141.4 sin (314 t + 10°)

This expression indicates a sinusoidally varying alternating voltage at a frequency

ω = 314 rad/sec, f = 50Hz

V = RMS voltage (Peak voltage)/√2 = 100volts

The expression for the current gives the following data :

I = RMS value = 14.14/√2 = 10 amp

frequency = 50 Hz, naturally.

Phase shift between I and V = 30°, I lags behind V.

(i) Power factor of the circuit = cos 30° = 0.866 lag

(ii) P = VI cos φ = 100 × 10 × 0.866 = 866 watts

(iii) Phasor diagram as drawn below, in Fig..