Question

For an R-L series circuit, the power factor is \(\frac{\sqrt{3}}{2}\), for a supply frequency of \(f\) Hz. If the frequency doubles, the new power factor will be

• A. \(\frac{3}{\sqrt{7}}\)
• B. \(\frac{\sqrt{3}}{7}\)
• C. \(\frac{3}{7}\)
• D. \(\sqrt{\frac{3}{7}}\)

Hint:

Use cos phi equals R over impedance to find the ratio of inductive reactance to resistance, then double the frequency.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
In an R-L circuit \(\cos\phi=\dfrac{R}{\sqrt{R^{2}+X_{L}^{2}}}\) and \(X_{L}=2\pi fL\).

Step 2: Find X_L in terms of R
\(\cos\phi=\dfrac{\sqrt{3}}{2}\) gives \(\tan\phi=\dfrac{1}{\sqrt{3}}\), so \(X_{L}=\dfrac{R}{\sqrt{3}}\).

Step 3: Double the frequency
The new reactance is \(X_{L}'=2X_{L}=\dfrac{2R}{\sqrt{3}}\).

Step 4: New power factor
\(\cos\phi'=\dfrac{R}{\sqrt{R^{2}+\frac{4R^{2}}{3}}}=\dfrac{1}{\sqrt{7/3}}=\sqrt{\dfrac{3}{7}}\)

Final Answer:
The new power factor is root of 3 by 7. \[ \boxed{\text{(D) }\sqrt{\dfrac{3}{7}}} \]