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