Question

The percentage increase in the impedance of an ac circuit, when its power factor changes form $1/2$ to $1/4$is (Resistance constant)-

• A. 100$\%$
• B. 86.6$\%$
• C. 90.8$\%$
• D. 66.6$\%$

Answer 1

The correct option is A 100$\%$

$powerfactorofanyACcircuitisgivenby$

$\cos \theta =\frac{R}{Z}$

$sofortwocaseswhereresis\tan ceRiscons\tan t$

$\frac{R}{Z_1}=\frac{1}{2}$

$Z_1=2R$

$alsowehave$

$\frac{R}{Z_2}=\frac{1}{4}$

$Z_2=4R$

$Nowthepercentagechangeinindependenceisgivenby$

$percentage=\frac{Z_2-Z_1}{Z_1}\times 100$

$percentage=\frac{4R-2R}{2R}\times 100=100$

$So,thereis100\%changeintheindependenceofthegivenACcircuit$

Hence,

option $\left(A\right)$ is correct answer.