Question

If the power factor in an AC circuit changesfrom $\frac{1}{3}$ to $\frac{1}{9}$ then by what percent reactance will change (approximately), if resistance remains constant?

• A. Increase by $200\%$
• B. Decrease by $200\%$
• C. Increase by $100\%$
• D. Decrease by $100\%$

Answer 1

Answer: (A)

Power factor $\cos \varphi =\frac{R}{Z}$
$\frac{R}{\sqrt{R^2+X^2}}=\frac{1}{3}$
$\frac{R}{\sqrt{R^2+{\left(X^{\prime }\right)}^2}}=\frac{1}{9}$
Using $(1)$ and $(2)$
$X=R\sqrt{8}$
$X^{\prime }=R\sqrt{80}$
$\frac{X^{\prime }}{X}=\sqrt{10}$
$\frac{X^{\prime }-X}{X}=(\sqrt{10}-1)$
so percentage change
$=(\sqrt{10}-1)\times 100$
$\cong 200\%$