Gate 2016 EE Set 2 - Question 36

In order to find the value of C, we arrange the capacitors in the same form as the inductors in the figure. Convert the capacitors arrangement from star to delta.

Line currents will be zero when the parallel pair of inductor capacitor is resonant at f=50Hz

$2\pi f=\frac{1}{\sqrt{\frac{LC}{3}}}\Rightarrow 100\pi =\frac{1}{\sqrt{\frac{LC}{3}}}$

$100\pi \sqrt{\frac{LC}{3}}=1$

$\sqrt{\frac{LC}{3}}=\frac{1}{100\pi }\Rightarrow C=\frac{3}{L}\left ( \frac{1}{100\pi } \right )^{2}$

$C=3.03\times 10^{-3}$

$C=3.03mF$