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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

L and C

C

R and C

D

only R

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of determining the components in 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 Relationship**: - In an AC circuit, if the current lags behind the voltage, it indicates that the circuit has inductive characteristics. The phase difference of \( \frac{\pi}{3} \) means that the voltage leads the current by this angle. 2. **Identifying Circuit Components**: - The components that can cause a phase difference between voltage and current are resistors (R), inductors (L), and capacitors (C). - In a purely resistive circuit, the current and voltage are in phase (phase difference = 0). - In a purely inductive circuit, the current lags the voltage by \( \frac{\pi}{2} \). - In a purely capacitive circuit, the current leads the voltage by \( \frac{\pi}{2} \). 3. **Analyzing the Given Phase Difference**: - Since the current lags the voltage by \( \frac{\pi}{3} \), we need to consider combinations of R and L that can produce this phase difference. - The presence of a resistor (R) in the circuit allows for a phase angle that is less than \( \frac{\pi}{2} \) when combined with an inductor (L). 4. **Considering the RL Circuit**: - In an RL circuit, the phase angle \( \phi \) can be calculated using the formula: \[ \tan(\phi) = \frac{X_L}{R} \] where \( X_L \) is the inductive reactance. - For \( \phi = \frac{\pi}{3} \): \[ \tan\left(\frac{\pi}{3}\right) = \sqrt{3} \] - This indicates that the circuit must have both R and L components to achieve this specific phase difference. 5. **Evaluating Other Combinations**: - For an LC circuit, the voltage across the inductor (V_L) and the capacitor (V_C) would lead to a phase difference of \( \frac{\pi}{2} \) or \( -\frac{\pi}{2} \), which does not match our requirement. - For an RC circuit, the current leads the voltage, which is opposite to what we need. 6. **Conclusion**: - The only combination of components that allows the current to lag behind the voltage by \( \frac{\pi}{3} \) is an RL circuit. ### Final Answer: The components in the circuit are **R and L** (Resistor and Inductor).
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