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# 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

Last updated date: 12th Sep 2024
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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).