A circuit contains R, L and C connected in series with an A. C. source. The values of the reactances for inductor and capacitor are `200Omega` and `600Omega` respectively and the impedance of the circuit is Z1 . What happens to the impedance of the same circuit if the values of the reactances are interchanged:-

Options

A. The impedance will remain unchanged
B. The impedance will increase
C. The impedance will decrease
D. The phase angle will remain unchanged

Answer

To solve the problem, we will analyze the impedance of a series RLC circuit with given reactances for the inductor and capacitor. We will also consider what happens when the reactances are interchanged.

### Step-by-step Solution:

1. **Identify the given values:**
- Reactance of the inductor \( X_L = 200 \, \Omega \)
- Reactance of the capacitor \( X_C = 600 \, \Omega \)

2. **Calculate the net reactance for the initial configuration:**
- In a series RLC circuit, the total reactance \( X \) is given by:
\[ X = X_L - X_C \]
- Substituting the values:
\[ X = 200 \, \Omega - 600 \, \Omega = -400 \, \Omega \]
- The negative sign indicates that the circuit is capacitive.

3. **Calculate the impedance \( Z_1 \) for the initial configuration:**
- The impedance \( Z \) in a series circuit is given by:
\[ Z = \sqrt{R^2 + X^2} \]
- Substituting for \( X \):
\[ Z_1 = \sqrt{R^2 + (-400)^2} = \sqrt{R^2 + 160000} \]

4. **Interchange the reactances:**
- Now, let’s interchange the reactances:
- New reactance of the inductor \( X_L' = 600 \, \Omega \)
- New reactance of the capacitor \( X_C' = 200 \, \Omega \)

5. **Calculate the net reactance for the new configuration:**
- Again, using the formula for total reactance:
\[ X' = X_L' - X_C' = 600 \, \Omega - 200 \, \Omega = 400 \, \Omega \]
- The positive sign indicates that the circuit is inductive.

6. **Calculate the impedance \( Z_2 \) for the new configuration:**
- The impedance for the new configuration is:
\[ Z_2 = \sqrt{R^2 + (400)^2} = \sqrt{R^2 + 160000} \]

7. **Compare the two impedances:**
- We find that:
\[ Z_1 = \sqrt{R^2 + 160000} \]
\[ Z_2 = \sqrt{R^2 + 160000} \]
- Therefore, \( Z_1 = Z_2 \).

### Conclusion:
The impedance of the circuit remains unchanged when the values of the reactances are interchanged.