What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

Solution

Physics sir · 4 steps

Reactance grows with frequency, so halving the frequency halves X_L, and the current doubles in turn.

1. Reactance depends on frequency. An inductor opposes a change in current. The faster the current changes, the stronger the opposition, so its reactance is directly proportional to frequency.

   X_L = ω L = 2π f L

2. Halve the frequency. With L fixed, replacing f by f/2 gives X_L' = 2π f/2 L = X_L/2. The reactance is halved.
3. Current follows. In a purely inductive circuit Iᵣₘₛ = Vᵣₘₛ/X_L. The supply voltage stays the same, so halving X_L makes the current twice as large.
4. So. The inductive reactance is halved and the current is doubled, which is option (d).

The idea to keep. For an inductor, X_L = 2π f L rises with frequency. For a capacitor, X_C = 1/(2π f C) falls with frequency. At fixed voltage, current always moves opposite to reactance.

Answer from the NTA final answer key. Solution by PrepWiser.