alleryStart learning →In a series RLC circuit, RESONANCE occurs at the frequency where
A$X_L = 0$
B$X_C = 0$
C$X_L = X_C$
D$R = 0$
Answer & Solution
Correct answer: C. $X_L = X_C$
1. Series RLC impedance: $Z = R + j(X_L - X_C) = R + j(\omega L - 1/(\omega C))$.
2. At RESONANCE: the imaginary part is zero → $X_L = X_C$, i.e. $\omega L = 1/(\omega C)$.
3. Solving: $\omega_0 = 1/\sqrt{LC}$, or $f_0 = 1/(2\pi\sqrt{LC})$.
4. At resonance, the circuit is PURELY RESISTIVE; impedance is minimum ($Z = R$); current is maximum.
5. Used in tuners, filters, oscillators.
6. Options A, B, D are not the resonance condition.
_Source: Tony Kuphaldt, "Lessons in Electric Circuits — AC", Vol II, Ch 6 (Resonance)._
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