MHT CET · Physics · Alternating Current
An a.c. source is applied to a series LR circuit with \(X_L=3 R\) and power factor is \(X_1\). Now a capacitor with \(X_C=R\) is added in series to LR circuit and the power factor is \(X_2\). The ratio \(X_1\) to \(X_2\) is
- A \(1: 2\)
- B \(2: 1\)
- C \(1: \sqrt{2}\)
- D \(\sqrt{2}: 1\)
Answer & Solution
Correct Answer
(C) \(1: \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(X_1 = \frac{R}{\sqrt{R^2 + X_L^2}} = \frac{R}{\sqrt{R^2 + (3R)^2}} = \frac{R}{\sqrt{10R^2}} = \frac{1}{\sqrt{10}}\) \(X_2 = \frac{R}{\sqrt{R^2 + (X_L - X_C)^2}} = \frac{R}{\sqrt{R^2 + (3R - R)^2}} = \frac{R}{\sqrt{R^2 + (2R)^2}} = \frac{R}{\sqrt{5R^2}} = \frac{1}{\sqrt{5}}\)
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