Question

The potential differences of the resistance, the capacitor and the inductor are $80V,40V$ and $100V$ respectively in an $L.C.R$ circuit. The power factor of the circuit is

• A. $1\cdot 0$
• B. $0\cdot 4$
• C. $0\cdot 5$
• D. $0\cdot 8$

Answer 1

The correct option is D $0\cdot 8$

The potential difference across an element in a circuit is given by $iX$.

Hence $80=iR$

$40=i{X}_C$

$100=i{X}_L$

Power factor of circuit=$cos\varphi =\frac{R}{Z}$

$=\frac{R}{\sqrt{(X_L-X_C{)}^2+R^2}}$
$=\frac{80}{\sqrt{(100-40{)}^2+{80}^2}}$

$=0.8$