Question

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

Short answer

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

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.

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.

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.

Choose the correct option

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