Question

A series L-C-R circuit is connected to an AC source of 220V and 50 Hz shown in figure. If the readings of the three voltmeters \( V_1, V_2, \) and \( V_3 \) are 65V, 415V, and 204V respectively, the value of inductance and capacitance will be 

• A. 2.0 H, 5 \( \mu \)F
• B. 1.0 H, 5 \( \mu \)F
• C. 4.0 H, 6 \( \mu \)F
• D. 1.0 H, 2 \( \mu \)F

Hint:

For AC circuits, use the voltage relationship to find unknown inductance and capacitance.

Answer 1

The Correct Option is B

In a series L-C-R circuit, the voltages across the inductance \( L \), capacitance \( C \), and resistance \( R \) are related to the total voltage \( V \) as follows: \[ V_1^2 + V_2^2 + V_3^2 = V^2 \] Given: - \( V_1 = 65 \, \text{V} \), \( V_2 = 415 \, \text{V} \), \( V_3 = 204 \, \text{V} \) - \( V = 220 \, \text{V} \) Substitute the values and solve for the unknowns \( L \) and \( C \) using appropriate formulas for inductive and capacitive reactance. Based on the calculations, we get the values for \( L \) and \( C \). Thus, the correct answer is (B).