JEE Main & Advanced Physics Electrostatics & Capacitance JEE PYQ-Electrostatics and Capacitance

Seven capacitors, each of capacitance \[2\mu F,\]are to be connected in a configuration to obtain an effective capacitance of \[\left( \frac{6}{13} \right)\mu F,\]Which of the combinations, shown in figures below, will achieve the desired value? [JEE Main 11-Jan-2019 Evening]

A)

B)

C)

D)

Correct Answer: A

Solution :

[a] \[{{C}_{1}}\]is given by

\[\frac{1}{{{C}_{1}}}=\frac{1}{3C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=\frac{1}{6}+\frac{4}{2}(\because C=2\mu F)\]

\[{{C}_{1}}=\frac{6}{13}\mu F\]

\[{{C}_{2}}\]is given by

\[\frac{1}{{{C}_{2}}}=\frac{1}{5C}+\frac{2}{C}=\frac{1}{10}+1=\frac{11}{10}\]

\[{{C}_{2}}=\frac{10}{10}\mu F\]

\[{{C}_{3}}\]is given by

\[\frac{1}{{{C}_{3}}}=\frac{1}{4C}+\frac{3}{C}=\frac{1}{8}+\frac{3}{2}=\frac{26}{16}=\frac{13}{8}\]

\[{{C}_{3}}=\frac{8}{13}\mu F\]

\[{{C}_{4}}\]is given by

\[\frac{1}{{{C}_{4}}}=\frac{1}{2C}+\frac{5}{C}=\frac{1}{4}+\frac{5}{2}=\frac{11}{4}\]

\[{{C}_{4}}=\frac{4}{11}\mu F\]