Power consumed in an AC circuit becomes zero if

Options

A. inductance and resistance are both high
B. inductance and resistance are both low
C. inductance very high and resistance negligible
D. inductance low and resistance high

Explanation

To determine when the power consumed in an AC circuit becomes zero, we need to analyze the relationship between resistance, inductance, and power consumption.

### Step-by-Step Solution:

1. **Understanding Power in AC Circuits**:
In an AC circuit, the power consumed is given by the formula:
\[ P = VI \cos(\phi) \]
where \( P \) is the power, \( V \) is the voltage, \( I \) is the current, and \( \phi \) is the phase difference between the voltage and current.

2. **Power Factor**:
The term \( \cos(\phi) \) is known as the power factor. If the circuit consists only of inductors and capacitors (LC circuit), the phase difference \( \phi \) can be \( 90^\circ \) (or \( \frac{\pi}{2} \) radians), leading to \( \cos(90^\circ) = 0 \). Thus, the power consumed becomes zero.

3. **Condition for Zero Power**:
The power consumed in an AC circuit becomes zero if:
- The circuit is purely inductive (only inductors) or purely capacitive (only capacitors).
- There is negligible resistance in the circuit.

4. **Analyzing Options**:
- **Option 1**: Inductance and resistance are both high.
- This option is incorrect because high resistance will consume power.
- **Option 2**: Resistance and inductance are both low.
- This option is incorrect because low resistance will still allow power consumption.
- **Option 3**: Inductance is very high and resistance is negligible.
- This option is correct because with negligible resistance and high inductance, the circuit behaves like an ideal inductor, leading to zero power consumption.
- **Option 4**: Inductance low and resistance high.
- This option is incorrect because high resistance will lead to significant power consumption.

5. **Conclusion**:
The most suitable answer is **Option 3**: Inductance is very high and resistance is negligible, which leads to zero power consumption in the AC circuit.