Question

In an RLC series circuit, at resonance, the impedance is:

• A. Minimum
• B. Maximum
• C. Equal to the sum of R, L, and C
• D. Zero

Hint:

At resonance in an RLC circuit, the impedance is at its minimum because the reactances of the inductor and capacitor cancel each other out.

Answer 1

The Correct Option is A

In an RLC series circuit, the impedance \( Z \) is given by: \[ Z = R + j \left( \omega L - \frac{1}{\omega C} \right) \] where \( R \) is the resistance, \( L \) is the inductance, \( C \) is the capacitance, and \( \omega \) is the angular frequency. At resonance, the inductive reactance \( \omega L \) and capacitive reactance \( \frac{1}{\omega C} \) are equal in magnitude but opposite in sign, so their effects cancel each other out, leaving only the resistance \( R \). Thus, at resonance, the impedance is: \[ Z = R \] This is the minimum impedance, so the correct answer is: \[ \boxed{(A) \, \text{Minimum}} \]