As the frequency of an ac circuit increases, the current first increases till it becomes maximum at resonance and then decreases. Which one of the following combinations of circuit elements are likely to comprise the circuit ?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → resistor, inductor and capacitor
In a series LCR circuit the current is \( I = V/\sqrt{R^{2} + (X_L - X_C)^{2}} \), with \( X_L = \omega L \) and \( X_C = 1/\omega C \). At low frequency \( X_C \) is large and the current is small; at high frequency \( X_L \) is large and the current is small again. In between, at the resonant frequency \( \omega_0 = 1/\sqrt{LC} \) where \( X_L = X_C \), the impedance is minimum (\( Z = R \)) and the current is maximum. A rise followed by a fall therefore needs both L and C, with R present to limit the peak.
Why the other options are incorrect
Option (1) capacitor only — Incorrect. \( I = V\omega C \) keeps increasing with frequency.
Option (3) inductor and resistor only — Incorrect. \( I = V/\sqrt{R^{2}+\omega^{2}L^{2}} \) only decreases as the frequency increases.
Option (4) resistor and capacitor only — Incorrect. The current increases with frequency and approaches \( V/R \), but never falls.
NCERT Exemplar:
Alternating Current – …
