If `omega` is angular frequency of a.c., then the reactance offered by inductance L and capacitance C are `X_(L)`……………………..and `X_(C )`……………

Answer

To solve the question regarding the reactance offered by inductance \( L \) and capacitance \( C \) in an alternating current (AC) circuit, we need to derive the expressions for the inductive reactance \( X_L \) and capacitive reactance \( X_C \).

### Step-by-Step Solution:

1. **Understanding Angular Frequency**:
- The angular frequency \( \omega \) is related to the frequency \( f \) of the AC circuit by the formula:
\[ \omega = 2\pi f \]

2. **Inductive Reactance**:
- The inductive reactance \( X_L \) is given by the formula:
\[ X_L = \omega L \]
- Here, \( L \) is the inductance. This formula indicates that the reactance increases with both the frequency of the AC and the inductance.

3. **Capacitive Reactance**:
- The capacitive reactance \( X_C \) is given by the formula:
\[ X_C = \frac{1}{\omega C} \]
- In this case, \( C \) is the capacitance. This formula shows that the reactance decreases with increasing frequency and increases with larger capacitance.

4. **Final Expressions**:
- Therefore, the reactance offered by inductance \( L \) is:
\[ X_L = \omega L \]
- And the reactance offered by capacitance \( C \) is:
\[ X_C = \frac{1}{\omega C} \]

### Summary:
- The reactance offered by inductance \( L \) is \( X_L = \omega L \).
- The reactance offered by capacitance \( C \) is \( X_C = \frac{1}{\omega C} \).