GATE 2022 IN – Question 52
The load shown is driven by $V_1=100\angle0^\circ$ V at 50 Hz. Given $R_1=20\ \Omega$, $C_1=(1000/\pi)$ μF, $L_1=(20/\pi)$ mH, and $R_2=4\ \Omega$, its power factor is ______ (one decimal place).
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Correct answer: 0.8 to 0.8
Explanation
At 50 Hz, XC=10 Ω and XL=2 Ω. Parallel 20 Ω and −j10 Ω gives 4−j8 Ω. Add R2=4 Ω and j2 Ω to get total 8−j6 Ω, magnitude 10 Ω. Power factor is 8/10=**0.8**, leading.