Power loss in `AC` circuit will be minimum when

Options

A. Inductance is high, resistance is high
B. Inductance is low, resistance is high
C. Inductance is low, resistance is low
D. Inductance is high, resistance is low

Explanation

To determine when the power loss in an AC circuit is minimized, we can analyze the relationship between the resistance (R), inductance (L), and the power loss formula.

### Step-by-Step Solution:

1. **Understanding Power Loss in AC Circuits**:
- The power loss (P) in an AC circuit primarily occurs in the resistive component. The formula for average power loss is given by:
\[ P = I^2 R \]
- Here, \(I\) is the current flowing through the circuit, and \(R\) is the resistance.

2. **Current in the Circuit**:
- The current (\(I\)) in the circuit can be expressed in terms of the applied voltage (\(V_{rms}\)) and the impedance (\(Z\)):
\[ I = \frac{V_{rms}}{Z} \]
- The impedance \(Z\) for an LC circuit is given by:
\[ Z = \sqrt{R^2 + (L \omega)^2} \]
- Where \(L\) is the inductance and \(\omega\) is the angular frequency.

3. **Substituting Current into Power Loss Formula**:
- Substituting \(I\) into the power loss formula gives:
\[ P = \left(\frac{V_{rms}}{Z}\right)^2 R \]
- This can be rewritten as:
\[ P = \frac{V_{rms}^2 R}{R^2 + (L \omega)^2} \]

4. **Analyzing the Power Loss**:
- To minimize power loss \(P\), we need to maximize the denominator \(R^2 + (L \omega)^2\).
- This can be achieved by increasing \(L\) (inductance) and minimizing \(R\) (resistance).

5. **Conclusion**:
- Therefore, the power loss in an AC circuit will be minimum when the inductance \(L\) is high and the resistance \(R\) is low.

### Final Answer:
The power loss in an AC circuit will be minimum when the inductance \(L\) is high and the resistance \(R\) is low.