Question

A circuit consisting of a capacitor and a coil in series is connected to the mains. Varying the capacitance of the capacitor, the horse power generated in the coil was increased n=1.7 times. How much $\%$ was the value of $cos\varnothing$ changed in the process?

• A. $80\%$
• B. $25\%$
• C. $50\%$
• D. $30\%$

Answer 1

Answer: (D)

R.E.F image

$P^1=1.7P$

${\left[\frac{V}{\sqrt{R^2+(X_c-X_c^1{)}^2}}\right]}^{2}R=1.7{\left[\frac{V}{\sqrt{R^2+(X_c-X_c{)}^2}}\right]}^{2}R$

$\Rightarrow \frac{1}{R^2+(X_c-X_c^1{)}^2}=\frac{1.7}{R^2+(X_c-X_c{)}^2}$

$\Rightarrow \frac{R^2}{R^2+(X_c-X_c^1{)}^2}=1.7\frac{R^2}{(R^2+(X_c-X_c{)}^2)}$

$\Rightarrow \frac{R}{\sqrt{R^2+(X_c-X_c^1{)}^2}}=\sqrt{1.7}\frac{R}{\sqrt{R^2+(X_c-X_c{)}^2}}$

$\Rightarrow cos{\theta }^1=\sqrt{1.7}cos\theta$

$\Rightarrow \%=\frac{cos{\theta }^1-cos\theta }{cos\theta }\times 100$ $=\frac{\sqrt{1.7}cos\theta -cos\theta }{cos\theta }\times 100$

$=\left(\sqrt{1.7-1}\right)100$

$=30.38\%$