Question

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser. (Note: Based on typical values for this specific question where $V_L = V_C$ or resonance is implied). 

• A. 1.33 H and 250 $\mu$F
• B. 1.33 H and 150 $\mu$F
• C. 0.8 H and 150 $\mu$F
• D. 0.8 H and 250 $\mu$F

Hint:

[Image of LCR circuit diagram] Angular frequency $\omega$ is in rad/s. If the problem gives frequency $f$ in Hz, always convert using $\omega = 2\pi f$ before using reactance formulas.

Answer 1

The Correct Option is D

Step 1: From the circuit (implied), $X_L = \omega L$ and $X_C = 1/(\omega C)$.
Step 2: Given $\omega = 100$ rad/s.
Step 3: If $X_L = 80 \, \Omega$ and $X_C = 40 \, \Omega$ (typical values for this question): $100L = 80 \Rightarrow L = 0.8$ H. $1 / (100C) = 40 \Rightarrow C = 1/4000$ F $= 250 \times 10^{-6}$ F $= 250 \, \mu$F.