Question

A series LCR circuit is shown in the figure. Where the inductance of 10 H, capacitance 40 \muF and resistance 60 Ω are connected to a variable frequency 240 V source. The current at resonating frequency is.
 

• A. 4 A
• B. 2 A
• C. 5.4 A
• D. 5.8 A

Hint:

At the resonating frequency in an LCR circuit, the impedance is equal to the resistance, and the current can be found using Ohm's law.

Answer 1

The Correct Option is A

At the resonating frequency, the inductive reactance \( X_L \) and capacitive reactance \( X_C \) are equal, and they cancel each other out. Thus, the total impedance \( Z \) of the LCR circuit is just the resistance \( R \), which is \( 60 \, \Omega \). Using Ohm's law: \[ I = \frac{V}{R} = \frac{240}{60} = 4 \, \text{A} \] Thus, the current at the resonating frequency is 4 A.