In an AC circuit, the current leads the voltage by \(\frac{\pi}{2}\) The circuit is _______.
Fill in the blank with the correct answer from the options given below
Fill in the blank with the correct answer from the options given below
- purely resistive
- should have circuit elements with resistance equal to reactance.
- purely inductive
- purely capacitive
The Correct Option is D
Approach Solution - 1
In an AC (Alternating Current) circuit, the phase difference between the current and voltage indicates the type of circuit component in operation. The phase difference, denoted in radians, helps to deduce the nature of the circuit being analyzed.
Given that the current leads the voltage by \(\frac{\pi}{2}\) radians, we identify the component responsible for this behavior:
1. Purely Resistive Circuit: In such circuits, the current and voltage are in phase, meaning there is no phase difference between them: \(\phi = 0\).
2. Purely Inductive Circuit: The voltage leads the current by \(\frac{\pi}{2}\) radians.
3. Purely Capacitive Circuit: The current leads the voltage by \(\frac{\pi}{2}\) radians.
4. Resistance Equal to Reactance: This is characteristic of an RLC circuit in resonance, where the total impedance is minimized, and phase differences would typically depend on the specific component values and frequency.
Based on these characteristics, when the current leads the voltage by \(\frac{\pi}{2}\) radians, the circuit must be purely capacitive. Therefore, the correct answer is purely capacitive.
Approach Solution -2
Let's analyze the relationship between current and voltage in AC circuits:
- Purely Resistive Circuit: In a purely resistive circuit, the current and voltage are in phase (phase difference = 0).
- Purely Inductive Circuit: In a purely inductive circuit, the voltage leads the current by π/2 (90°).
- Purely Capacitive Circuit: In a purely capacitive circuit, the current leads the voltage by π/2 (90°).
- RL or RC Circuits: In circuits with both resistance and inductance or capacitance, the phase difference is between 0 and π/2.
Given that the current leads the voltage by π/2, the circuit must be purely capacitive.
The correct answer is:
Option 4: purely capacitive
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