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

The following procedure determines the impedance, resistance, capacitive reactance, and inductive reactance for a series LCR circuit.

1. Provided parameters: \(E=30\sin(100t)\), \(R=120\Omega\), \(L=100\text{ mH}\), \(C=100\mu\text{F}\). Angular frequency \(\omega=100\text{ rad/s}\).
2. Inductive Reactance Calculation \((X_L)\):
   \(X_L=\omega L=100 \times 0.1=10\Omega\).
3. Capacitive Reactance Calculation \((X_C)\):
   \(X_C=\frac{1}{\omega C}=\frac{1}{100 \times 100 \times 10^{-6}}=100\Omega\).
4. Impedance Calculation \((Z)\):
   \(Z=\sqrt{R^2+(X_L-X_C)^2}=\sqrt{120^2+(10-100)^2}=\sqrt{120^2+(-90)^2}=\sqrt{14400+8100}=\sqrt{22500}=150\Omega\).

The calculated values are:
(A) Impedance = 150Ω,
(B) Resistance = 120Ω,
(C) Capacitive Reactance = 100Ω,
(D) Inductive Reactance = 10Ω.

When arranged in ascending order, the sequence is: (D), (C), (B), (A).