Question

In series LCR resonant circuit, R \(=800 \Omega\), \(\mathrm{C}=2 \mu \mathrm{~F}\) and voltage across resistance is 200 V . The angular frequency is \(250 \mathrm{rad} / \mathrm{s}\). At resonance, the voltage across the inductance is

• A. 400 V
• B. 250 V
• C. 1000 V
• D. 500 V

Hint:

At resonance X_L equals X_C, so the voltage across L equals the voltage across C.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
At resonance \(X_L=X_C=\dfrac{1}{\omega C}\) and the current is \(I=\dfrac{V_R}{R}\).

Step 2: Current
\(I=\dfrac{200}{800}=0.25\text{ A}\)

Step 3: Calculation
\(X_L=X_C=\dfrac{1}{250\times2\times10^{-6}}=2000\ \Omega\)
\(V_L=I X_L=0.25\times2000=500\text{ V}\)

Final Answer:
The voltage across the inductor is 500 V. \[ \boxed{\text{(D) }500\ \text{V}} \]