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So we write Power factor is  p \cdot f=\cos \phi=\frac{R}{Z}=\frac{R}{\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}}so we get, p \cdot f=\frac{60}{\sqrt{60^{2}+\left(2 \pi(60)(0.5)-\frac{1}{2 \pi(60)\left(30 \times 10^{-6}\right)}\right)^{2}}}so we get, p . f=0.52 Option e) is correct choice.   ...