NEETPhysicsAlternating Current
An AC source of variable frequency is connected in series with a light bulb and an ideal inductor. If the frequency of the AC source is gradually increased while keeping the voltage amplitude constant, what happens to the inductive reactance and the brightness of the bulb?
Options
- AInductive reactance decreases and the brightness of the bulb increases.
- BInductive reactance increases and the brightness of the bulb increases.
- CInductive reactance increases and the brightness of the bulb remains constant.
- DInductive reactance increases and the brightness of the bulb decreases.
Correct answer
D. Inductive reactance increases and the brightness of the bulb decreases.
Step-by-step solution
The inductive reactance of an ideal inductor is given by X_L = 2 f L , where f is the frequency of the AC source. As the frequency f increases, the inductive reactance X_L increases. The total impedance of the series circuit is Z = R^2 + X_L^2 , where R is the resistance of the bulb. An increase in X_L leads to an increase in the total impedance Z . Since the voltage amplitude is constant, the RMS current in the circuit I_ rms = V_ rms Z will decrease. The brightness of the bulb depends on the power dissipated by i