Question

To a highly inductive circuit, a small capacitance is added in series. The angle between voltage and current will,

• A. increase
• B. decrease
• C. remain nearly same
• D. become indeterminant

Hint:

In series AC circuits, inductive and capacitive reactances oppose each other. Adding capacitance to an inductive circuit always reduces the phase angle.

Answer 1

The Correct Option is B

In a series circuit the phase angle is set by the ratio of net reactance to resistance, \(\phi=\tan^{-1}(X_{net}/R)\).

1. Increase: Would need the net reactance to grow, but a series capacitor works against the existing inductive reactance, not with it.
2. Decrease: A series capacitive reactance subtracts from the inductive reactance already present, shrinking \(X_{net}\) and hence \(\phi\).
3. Remain nearly same: Only true if the added capacitance were negligible, which isn't the case for a capacitance large enough to be worth adding.
4. Become indeterminate: The direction of change is fixed by the subtraction of reactances, not left uncertain.

So the angle between voltage and current decreases.

Answer 2

The same result can be seen through the power triangle instead of the impedance triangle. In a highly inductive circuit, the reactive power is large and mostly inductive (lagging), giving a large angle between the apparent power and the real power axis. Adding series capacitance introduces a leading reactive power component that partially offsets the inductive reactive power, shrinking the net reactive power relative to the real power.

1. Increase: This would need the net lagging reactive power to grow, but the capacitor's contribution works in the opposite (leading) direction.
2. Decrease: Since the capacitor's leading reactive power partially cancels the existing lagging reactive power, the net reactive power shrinks relative to the real power, and the power-triangle angle (which equals the voltage-current phase angle) decreases.
3. Remain nearly same: Would require the capacitor's effect to be negligible, which contradicts the premise of adding a capacitance that is meant to matter.
4. Become indeterminate: The offsetting effect of a capacitive element on an inductive circuit's reactive power is a fixed, predictable direction, not an indeterminate one.

Therefore, the correct answer is decrease.