Question

1. The voltage across the load is v(t)=100 Cos(314-35) and the current through the load
is i(t)=40 Cos(314t+10).
a. Find the power factor.
b. Draw the phasor diagram for the two vectors.

please Answer ASAP​

Answer 1

Power factor of the circuit = cos 45° = 0.707

Given that;

The voltage across the load is v(t)=100 Cos(314-35) and the current through the load is i(t)=40 Cos(314t+10).

To find;

a. The power factor.

b. The phasor diagram for the two vectors.

Solution;

v(t) =  v(t)=100 Cos(314-35)

This expression indicates a sinusoidal varying alternating voltage at a frequency

 ω = 314 rad/sec, f = 50Hz

V = RMS voltage (Peak voltage)/√2 = 70.92v

The expression for the current gives the following data :

 I = RMS value = 40/√2 = 28.28 amp

 frequency = 50 Hz, naturally

Phase shift between I and V = 45°, I is ahead of V.

Power factor of the circuit = cos 45° = 0.707 ahead.

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