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In an ac circuit, the current lags behin...

In an ac circuit, the current lags behind the voltage by `pi//3`. The components in the circuit are

A

R and L

B

R and C

C

L and C

D

Only R

Text Solution

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The correct Answer is:
To determine the components of an AC circuit where the current lags behind the voltage by \( \frac{\pi}{3} \), we can analyze the situation step by step. ### Step-by-Step Solution: 1. **Understanding Phase Difference**: - In an AC circuit, the phase difference between current and voltage indicates the type of components present. If the current lags behind the voltage, it suggests the presence of inductive components. **Hint**: Recognize that a lagging current indicates an inductive reactance. 2. **Identifying Components**: - The voltage across a resistor (R) is in phase with the current. The voltage across an inductor (L) leads the current by \( \frac{\pi}{2} \) (90 degrees), while the voltage across a capacitor (C) lags the current by \( \frac{\pi}{2} \) (90 degrees). **Hint**: Recall the phase relationships for R, L, and C in AC circuits. 3. **Analyzing the Given Phase Difference**: - Since the current lags the voltage by \( \frac{\pi}{3} \), we need to find a combination of R and L that results in this specific phase difference. The voltage across R and L must combine to produce a net voltage that leads the current by \( \frac{\pi}{3} \). **Hint**: Use phasor diagrams to visualize the relationships between voltage and current. 4. **Using Phasor Representation**: - In a series R-L circuit, the total voltage \( V \) can be represented as the vector sum of the voltage across the resistor \( V_R \) and the voltage across the inductor \( V_L \). The net voltage will be in the first quadrant if both components are present. **Hint**: Remember that the vector sum of voltages must yield the correct phase angle. 5. **Conclusion on Components**: - The only configuration that allows for the current to lag the voltage by \( \frac{\pi}{3} \) is a combination of a resistor (R) and an inductor (L). A purely resistive or capacitive circuit would not produce this lagging behavior. **Hint**: Conclude that the presence of both R and L is necessary to achieve the specified phase difference. ### Final Answer: The components in the circuit are a **Resistor (R)** and an **Inductor (L)**.
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