Question

Assertion $(A)$ If the frequency of the applied AC is doubled, then the power factor of a series $R-L$ circuit decreases.
Reason $(R)$ Power factor of series $R$ - $L$ circuit is given by $\cos \theta=\frac{2 R}{\sqrt{R^{2}+\omega^{2} L^{2}}}$

• A. If both Assertion and Reason are true and Reason is correct explanation of Assertion.
• B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
• C. If Assertion is true but Reason is false.
• D. If both Assertion and Reason are false.

Answer 1

Answer: (C)

Power factor of series $R$ - $L$ circuit is given by
$\cos \phi=\frac{R}{Z}=\frac{R}{\sqrt{R^{2}+\omega^{2} L^{2}}}$
when frequency becomes double
$ \cos \phi'=\frac{R}{\sqrt{R^{2}+4 \omega^{2} L^{2}}}$
$ \Rightarrow \cos \phi' < \cos \phi $