A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R = 80 Ω, an inductor of inductive reactance XL = 70 Ω, and a capacitor of capacitive reactance XC = 130 Ω. The power factor of circuit is x/10. The value of x is: Numerical answer type. Work it out, then open the answer.

Answer: 8. Z = √(80² + (130 - 70)²) = √(6400 + 3600) = 100 Ω. cos φ = R/Z = 80/100 = 8/10. So x = 8.

A series LCR circuit is connected to an AC source of 220 V, 50 Hz… | JEE Main 2023 (25 Jan, Shift 2)

Q47JEE Main 2023 · 25 JAN · SHIFT 2Medium

Power, Power Factor & Wattless Current

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R = 80 $\Omega$ , an inductor of inductive reactance $X_L = 70\ \Omega$ , and a capacitor of capacitive reactance $X_C = 130\ \Omega$ . The power factor of circuit is $\frac{x}{10}$ . The value of $x$ is:

Numerical answer type. Work it out, then open the answer.

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Answer: 8

$Z = \sqrt{80^2 + (130 - 70)^2} = \sqrt{6400 + 3600} = 100\ \Omega$ .
$\cos\phi = \frac{R}{Z} = \frac{80}{100} = \frac{8}{10}$ .
So $x = 8$ .

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