Question

An AC circuit draws 5A at 160 V and the power consumption is 600 W. Then the power factor is:
(A) 1
(B) 0.75
(C) 0.5
(D) 0

Answer 1

Hint: We are given an AC circuit. AC circuit involves alternating current and voltage. Given us the values of current, voltage and net power consumption. We need to find the power factor. Had this not been alternating, the current power factor would not have existed.

Complete step by step answer:
The given values are;
Current, I= 5A
Voltage, v= 160 V
Power, P= 600 W
We know in an AC circuit power consumed is given by the formula,
\[\Rightarrow P={{V}_{RMS}}{{I}_{RMS}}\cos \alpha \]
Here we are given the RMS values only in the question and not the peak values, so w o does not have to make any conversions. Here \[\alpha \]is the angle between the current phasor and the voltage phasor in the given circuit. Putting the values, we get
\[\begin{align}
&\Rightarrow P={{V}_{RMS}}{{I}_{RMS}}\cos \alpha \\
&\Rightarrow 600=160\times 5\times \cos \alpha \\
&\therefore \cos \alpha =\frac{600}{800}=0.75 \\
\end{align}\]

The value \[\cos \alpha \] is the required power factor and its value is 0.75. So, the correct option is (B).

Additional information:
For us to calculate the total power consumed, we need to know the phase difference between the sinusoidal waveforms of the voltage and current. In an AC circuit, the current and voltage values are sinusoidal so they are constantly changing with the time

Note:Here we should keep in mind that problems involving LCR circuits or alternating voltages and currents, then the values given in the question of voltage and current are always RMS and not peak values.