When Ø is the phase difference, what is the power factor?a)tan Øb)cosh Øc)cos Ød)sin ØCorrect answer is option 'C'. Can you explain this answer?

Question

When &#216; is the phase difference, what is the power factor?&#8203;a)tan &#216;b)cosh &#216;c)cos &#216;d)sin &#216;Correct answer is option 'C'. Can you explain this answer?

Answer

Cos Ø is called a power factor that indicates what fraction of [(Voltage V) x (Current I)] becomes the useful power. Most electric circuits have resistance and inductance. In such electric circuit, the current lags the voltage by the phase difference.

Answer

Cos Ø is called a power factor that indicates what fraction of [(Voltage V) x (Current I)] becomes the useful power. Most electric circuits have resistance and inductance. In such an electric circuit, the current lags the voltage by the phase difference.

Answer

The power factor is defined as the ratio of the real power to the apparent power in an AC circuit. It is a dimensionless quantity that ranges from 0 to 1. The power factor indicates the efficiency of power utilization in the circuit.

Phase Difference:
The phase difference refers to the difference in phase between two sinusoidal waveforms. In the context of power factor, it specifically refers to the phase difference between the voltage and current waveforms in an AC circuit.

Explanation:
The power factor is given by the cosine of the phase angle between the voltage and current waveforms. Mathematically, it can be expressed as:

Power Factor = cos(θ)

where θ is the phase angle.

Reasoning:
The power factor is given by the cosine function because it takes into account both the magnitude and phase angle of the waveforms. The cosine function provides a measure of the alignment between the voltage and current waveforms.

When the voltage and current waveforms are in phase (i.e., the phase difference is zero), the power factor is 1, indicating maximum power utilization. In this case, the voltage and current peaks occur at the same time, resulting in maximum power transfer.

When there is a phase difference between the voltage and current waveforms, the power factor is less than 1. This indicates that the power utilization is less efficient. The power factor decreases as the phase difference increases.

The cosine function is used instead of other trigonometric functions because it specifically considers the phase angle between the waveforms. The sine function, for example, only considers the magnitude of the waveforms and does not account for the phase difference.

In summary, the power factor is given by the cosine function because it considers both the magnitude and phase angle of the voltage and current waveforms in an AC circuit.

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