Question

In a series LCR circuit, the resistance (R), inductive reactance \(X_{L}=2R\) and capacitive reactance \(X_{C}=R\). The impedance of the circuit is

• A. \(R\)
• B. \(2R\)
• C. \(2^{0.5}R\)
• D. \(3^{0.5}R\)

Hint:

Impedance is the square root of R squared plus the square of the difference of the reactances.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For a series LCR circuit, \(Z=\sqrt{R^2+(X_L-X_C)^2}\).

Step 2: Calculation
\(X_L-X_C=2R-R=R\).

Step 3: Result
\(Z=\sqrt{R^2+R^2}=\sqrt{2}\,R=2^{0.5}R\).

Final Answer:
The impedance is root 2 times R. \[ \boxed{\text{(C) }2^{0.5}R} \]