Final answer:
When a variable frequency AC source is connected to a capacitor, the displacement current through the capacitor increases with a decrease in frequency. Option A is correct.
Step-by-step explanation:
When a variable frequency AC source is connected to a capacitor, the displacement current through the capacitor depends on the frequency of the source.
The displacement current is given by the equation:
I = C ΔV/Δt
Where I is the displacement current, C is the capacitance, ΔV is the change in voltage across the capacitor, and Δt is the change in time.
As the frequency decreases, the change in time Δt increases, which leads to an increase in the displacement current through the capacitor.
Therefore, the answer is A. increase.