Question

If the power factor of an $AC$ circuit changes from $\frac{1}{3}$ to $\frac{1}{9}$ then by what percentage 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

The correct option is A Increase by $200$%

$\begin{array}{c}\cos \varnothing =\frac{R}{Z}\\ \cos eI,Rincons\tan t\\ \frac{R}{Z_1}=\frac{1}{3}\Rightarrow Z_2=9R,X_{2‘}=\sqrt{81R^2-R^2}\\ \Rightarrow X_2=\sqrt{80R^2}\Rightarrow 2R\sqrt{20}\end{array}$

$\Rightarrow 50\%$

change

$=\frac{2R\sqrt{20}-2R\sqrt{2}}{2R\sqrt{2}}x200\%$