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

A series LCR circuit is connected to an AC source of 220 V,… — JEE Main 2023 Physics PYQ

JEE Main 2023 · 25 Jan · Shift 2 · numerical answer

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 :

Show answer and solution

Answer: 8

Solution

The net reactance is X_L - X_C = 70 - 130 = -60 Ω, so the impedance is Z = √(R² + (X_L - X_C)²) = √(80² + 60²) = √(6400 + 3600) = √10000 = 100 Ω.

Power factor = R/Z = 80/100 = 0.8 = 8/10, so x = 8.

[JEE Main 2023 · 25 Jan · Shift 2]

Practise Electromagnetic Induction and AC the way it is asked

A timed set of real JEE Main Electromagnetic Induction and AC questions, graded as the exam grades. No sign-up.

Start a Electromagnetic Induction and AC test

More: all JEE Main Electromagnetic Induction and AC questions · JEE Main 2023 · Physics chapter list

JEE Main 2023 Physics question on Electromagnetic Induction and AC