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 θ=(2 R/√R2+ω2 L2)

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 θ=(2 R/√R2+ω2 L2) (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.

Tardigrade Admin · Accepted Answer

Power factor of series R - L circuit is given by cos φ=(R/Z)=(R/√R2+ω2 L2) when frequency becomes double cos φ'=(R/√R2+4 ω2 L2) ⇒ cos φ' < cos φ

Q. 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 $cos θ = \frac{2 R}{R ^{2} + ω ^{2} L ^{2}}$

If both Assertion and Reason are true and Reason is correct explanation of Assertion.

If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

If Assertion is true but Reason is false.

If both Assertion and Reason are false.

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

Q. 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 cosθ=R2+ω2L2​2R​