Wattless current is obtained

Options

A. when resistance is zero
B. when current in minimum
C. when inductance is zero
D. when current is alternating current

Answer

To understand how wattless current is obtained, we need to delve into the concepts of alternating current (AC) circuits, particularly focusing on the relationship between voltage, current, and resistance.

### Step-by-Step Solution:

1. **Understanding Wattless Current**:
- Wattless current, also known as reactive current, occurs in an AC circuit when the power factor is zero. This means that the current and voltage are out of phase by 90 degrees (π/2 radians), resulting in no real power being consumed.

2. **Power Factor and Phase Angle**:
- The power factor (cos φ) is defined as the cosine of the phase angle (φ) between the current and voltage. For wattless current, we set cos φ = 0, which implies that φ = 90 degrees.

3. **Condition for Wattless Current**:
- In an AC circuit, wattless current can occur when the circuit is purely inductive or capacitive. This means:
- For a purely inductive circuit: The voltage leads the current by 90 degrees.
- For a purely capacitive circuit: The current leads the voltage by 90 degrees.
- In both cases, the average power (P) consumed is zero, which is the condition for wattless current.

4. **Mathematical Representation**:
- The average power in an AC circuit is given by:
\[ P = I_{\text{rms}} \cdot V_{\text{rms}} \cdot \cos \phi \]
- Since cos φ = 0 for wattless current, we find that:
\[ P = I_{\text{rms}} \cdot V_{\text{rms}} \cdot 0 = 0 \]
- Thus, no real power is consumed in the circuit.

5. **Conclusion**:
- Therefore, wattless current can be obtained in an AC circuit when the phase difference between the voltage and current is 90 degrees. This can occur in circuits with either zero resistance (ideal inductors or capacitors) or in circuits where the resistance is not dominant compared to the reactance.