Question

\(L=50\,mH,\; C=100\,\mu F,\; R=50\,\Omega\). What does this circuit represent? (Assume \(\omega=200\,rad/s\))

• A. Inductive circuit
• B. Capacitive circuit
• C. Resonant circuit
• D. Purely resistive circuit

Hint:

For an LCR circuit, first calculate \[ X_L=\omega L \] and \[ X_C=\frac{1}{\omega C}. \] Then compare them: \[ \boxed{ \begin{aligned} X_L\gt X_C &\Rightarrow \text{Inductive},\\ X_L\lt X_C &\Rightarrow \text{Capacitive},\\ X_L=X_C &\Rightarrow \text{Resonance}. \end{aligned} } \] At resonance, \[ \boxed{\omega=\frac{1}{\sqrt{LC}}} \] and the impedance is equal to the resistance only.

Answer 1

The Correct Option is C

At resonance in an LCR circuit, $X_L = X_C$, so the inductive and capacitive reactances cancel and the net impedance is purely resistive: $Z = R = 50\,\Omega$. The resonant frequency is $f_0 = 1/(2\pi\sqrt{LC})$.