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Chapter 14: Problem 2090

The power factor of a good choke coil is (a) Nearly zero (b) Exactly zero (c) Nearly one (d) Exactly one

Short Answer

Expert verified
The power factor of a good choke coil is (a) nearly zero, as it has very large inductive reactance (XL) compared to its resistance (R), making the ratio \(PF = \frac{R}{X_L}\) very small or close to zero.

Step by step solution

01

Analyze the given formula

Recall the power factor formula: \(PF = \frac{R}{\sqrt{R^2 + X_L^2}}\) As a good choke coil has very large inductive reactance (XL) compared to its resistance (R), we can deduce that: \(X_L >> R\) Now, let's analyze the power factor formula with this condition.
02

Apply the condition and evaluate the formula

Since \(X_L >> R\), we can consider \(R^2 + X_L^2 \approx X_L^2\). So, the power factor formula becomes: \(PF = \frac{R}{\sqrt{X_L^2}}\) We notice that the denominator now becomes an absolute inductive reactance value, which is significantly larger than resistance.
03

Compare the numerator and denominator

Now, we can simplify the formula: \(PF = \frac{R}{X_L}\) Given that the inductive reactance of a good choke coil (XL) is very large compared to its resistance (R), we can deduce that the ratio of R to XL will be very small or close to zero.
04

Choose the correct option

Since the power factor is very small or close to zero, the correct answer is (a) nearly zero.

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