A resistor, a capacitor and an inductor are joined in series with an alternating current source. If the frequency of the source is slightly increased from a very low value, then:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → inductive reactance increases
Reactance is the opposition of an inductor or a capacitor to alternating current, and it depends on the frequency \( \nu \) in opposite ways for the two.
\( X_{L} = 2\pi\nu L \quad (\text{grows with } \nu) \)
\( \displaystyle X_{C} = \frac{1}{2\pi\nu C} \quad (\text{falls as } \nu \text{ grows}) \)
\( \displaystyle Z = \sqrt{R^{2} + (X_{C} - X_{L})^{2}} \)
Option (1) resistance of resistor decreases — Incorrect. The resistance of a resistor does not depend on the frequency of the source.
Option (2) capacitive reactance increases — Incorrect. \( X_{C} \) is inversely proportional to the frequency, so it decreases as the frequency rises.
Option (3) inductive reactance increases — Correct. \( X_{L} \) is directly proportional to the frequency, so it increases as the frequency rises.
Option (4) impedance increases — Incorrect. At a very low frequency \( X_{C} \) is very large and \( X_{C} - X_{L} \) is large. Raising the frequency moves the circuit towards resonance, where \( X_{C} = X_{L} \), so the impedance decreases.
NCERT (2026-27):
AC Voltage Applied to an Inductor – “… The inductive reactance is directly proportional to the inductance and to the frequency of the current.”
AC Voltage Applied to a Capacitor – “… The capacitive reactance limits the amplitude of the current in a purely capacitive circuit in the same way as the resistance limits the current in a purely resistive circuit. But it is inversely proportional to the frequency and the capacitance.”