If the current in a coil lags the voltage by 60°, what is the circuit’s power factor?
0.5 lagging
To determine the power factor of the circuit, we need to understand the relationship between the phase angle and power factor.
The power factor (PF) in an AC circuit is given by the cosine of the phase angle (\(\phi\)) between the circuit voltage and current. Mathematically, it is represented as:
\(\text{Power Factor (PF)} = \cos(\phi)\)
Here, the given phase angle is 60°, where the current lags the voltage by 60°. Hence, \(\phi = 60^\circ\).
Now, substituting the value of \(\phi\) into the formula:
\(\text{PF} = \cos(60^\circ)\)
We know from trigonometric values that:
\(\cos(60^\circ) = 0.5\)
This indicates that the power factor is \(0.5\). Since the current lags the voltage, the nature of the power factor is lagging:
The correct answer is: 0.5 lagging.
Let's examine why other options are incorrect:
- √3/2 leading: This option would apply if the power factor was calculated as √3/2 and leading, which it is not.
- √3/2 lagging: Similarly, this is incorrect as our calculation showed the power factor as 0.5, not √3/2.
- 0.5 leading: This would occur if the phase angle was -60°, resulting in a leading power factor, which is not the case here.
Hence, the final answer aligns with the given correct answer.
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