KVPY Sample Paper KVPY Stream-SX Model Paper-6

In the circuit shown, find C if the effective capacitance of the whole circuit is to be \[0.5\mu F.\] All values in the circuit are in \[\mu F.\]

A) \[\frac{7}{11}\mu F\]

B) \[\frac{6}{5}\mu F\]

C) \[4\mu F\]

D) \[\frac{7}{10}\mu F\]

Correct Answer: A

Solution :

\[{{C}_{eq}}=0.5\mu F=\frac{\left( 1+\frac{4}{3} \right)C}{\frac{7}{3}+C}=\frac{7C}{\frac{7}{3}+C}=\frac{1}{2}\]

\[\Rightarrow \] \[\frac{14C}{3}=C+\frac{7}{3}\]

\[C=\frac{7}{11}.\]