In a circuit L,C and R are connected in series with an altematng voltage source of frequency f. The current leads the voltage by 60degree. The value of `(X_c -X_L)` is

Options

A. `sqrt3R`
B. `sqrt2R`
C. `1/sqrt3R`
D. 2R

Answer

To solve the problem, we need to find the value of \(X_C - X_L\) in a series LCR circuit where the current leads the voltage by \(60^\circ\).

### Step-by-Step Solution:

1. **Understand the Phase Relationship**:
In a series LCR circuit, if the current leads the voltage by \(60^\circ\), it indicates that the circuit is predominantly capacitive. This means that the capacitive reactance \(X_C\) is greater than the inductive reactance \(X_L\).

2. **Use the Phase Angle**:
The phase angle \(\phi\) is given as \(60^\circ\). We know that:
\[ \tan(\phi) = \frac{X_C - X_L}{R} \]
For \(\phi = 60^\circ\):
\[ \tan(60^\circ) = \sqrt{3} \]
Therefore, we can write:
\[ \sqrt{3} = \frac{X_C - X_L}{R} \]

3. **Rearranging the Equation**:
From the above equation, we can express \(X_C - X_L\) as:
\[ X_C - X_L = R \cdot \sqrt{3} \]

4. **Conclusion**:
Thus, the value of \(X_C - X_L\) is:
\[ X_C - X_L = R\sqrt{3} \]

### Final Answer:
The value of \(X_C - X_L\) is \(R\sqrt{3}\).