Question

The rms readings of voltmeters $V_1,V_2,V_3$ are $150V,130$ $V$ and $120V$, respectively. If the power factor of the circuit is $\frac{a}{\sqrt{b}}$, then find $(ab)$.

Answer 1

Answer: 30

$V_L^2+R_R^2=150^2$
$\Rightarrow V_L^2=150^2-120^2$
$\Rightarrow V_L=90V$
Also, $V_C^2+V_R^2=130^2$
$\Rightarrow V_C=50V$
$\therefore V=\sqrt{V_R^2+{\left(V_L-V_C\right)}^2}$
$=\sqrt{120^2+40^2}=40\sqrt{10}V$
Power factor, $\cos \varphi =\frac{R}{Z}=\frac{V_R}{V}$
$=\frac{120}{40\sqrt{10}}=\frac{3}{\sqrt{10}}$