Question

In an LCR circuit, inductive reactance is $30\ \Omega$ and capacitive reactance is $30\ \Omega$. The resistance is found to be $40\ \Omega$. The probable impedance of the combination is

• A. $60\ \Omega$
• B. $20\ \Omega$
• C. $100\ \Omega$
• D. $40\ \Omega$

Hint:

At resonance, inductive and capacitive reactances cancel, leaving only resistance as impedance.

Answer 1

The Correct Option is D

Step 1: Write the impedance formula.
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] Step 2: Substitute the given values.
\[ X_L = 30\ \Omega,\quad X_C = 30\ \Omega,\quad R = 40\ \Omega \] Step 3: Calculate reactance difference.
\[ X_L - X_C = 0 \] Step 4: Calculate impedance.
\[ Z = \sqrt{40^2} = 40\ \Omega \]