Power, Power Factor & Wattless Current question from MHT CET 2025 (25 Apr, Shift 1)

Answer: (b)

1. $\cos\phi = \frac{R}{\sqrt{R^2 + X_C^2}} = \frac{1}{\sqrt{2}} \Rightarrow X_C = R$.
2. $X_C = \frac{1}{2\pi fC}$, so halving $f$ doubles it: $X_C' = 2R$.
3. $\cos\phi' = \frac{R}{\sqrt{R^2 + 4R^2}} = \frac{1}{\sqrt{5}}$.
4. So the answer is (b) $\frac{1}{\sqrt{5}}$.