gate 2017 EE(Set-B) q40-solution

$$V_{or}=\frac{V_m}{2}$$
$$V_m=\sqrt{2V_s}$$
$$I_{or}=\frac{V_{or}}{R}=\frac{V_m}{2R}$$
$$\frac{V_m}{2}=\frac{\sqrt{2}}{2}V_s=\frac{V_s}{\sqrt{2}}$$
IPF $$=\frac{P_{load}}{inputVA}=\frac{V_{or}I_{or}}{V_SI_{or}}=\frac{V_{or}}{V_s}=\frac{V_s}{\sqrt{2}V_s}=\frac{1}{\sqrt{2}}=0.707$$