Question

In an LCR series circuit, the source of emf is E=30sin(100t), R=120Ω, L=100mH, C=100μF.
(A) The numerical value of impedance 
(B) The numerical value of resistance R 
(C) The numerical value of capacitive reactance 
(D) The numerical value of inductive reactance.
Arrange the values of quantities mentioned in (A, B, C, D) in increasing order.

• A. (A), (B), (C), (D)
• B. (A), (C), (B), (D)
• C. (D), (C), (B), (A)
• D. (B), (A), (D), (C)

Answer 1

The Correct Option is C

Given LCR circuit parameters:

E = 30sin(100t) V, R = 120 Ω, L = 100 mH, C = 100 μF

1. Angular frequency (ω): \[ ω = 100\ \text{rad/s} \] (from the source equation)

2. Inductive reactance (X_L): \[ X_L = ωL = 100 × 0.1 = 10\ \Omega \]

3. Capacitive reactance (X_C): \[ X_C = \frac{1}{ωC} = \frac{1}{100 × 100×10^{-6}} = 100\ \Omega \]

4. Impedance (Z): \[ Z = \sqrt{R^2 + (X_C - X_L)^2} = \sqrt{120^2 + (100 - 10)^2} \] \[ Z = \sqrt{14400 + 8100} = \sqrt{22500} = 150\ \Omega \]

Values obtained:

A. Impedance (Z) = 150 Ω

B. Resistance (R) = 120 Ω

C. Capacitive reactance (X_C) = 100 Ω

D. Inductive reactance (X_L) = 10 Ω

Increasing order: D (10 Ω) < C (100 Ω) < B (120 Ω) < A (150 Ω)

Final answer: The values in increasing order are D < C < B < A.