Some capacitors each of capacitance $30 μ F$ are connected as shown in figure. Calculate the equivalent capacitance (in $μ F$ ) between terminals $A$ and $B$ .

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Solution

let the total charge flowing through the circuit be Q and $Q_{1}, Q_{2}, Q_{3}$ in first loop
$Q = Q_{1} + Q_{2}$
loop ACDA : $Q_{1} = Q_{2} + Q_{3}$
loop DCED: $Q_{3} + Q_{2} - Q_{2} + 2 Q_{3} = Q_{2} - Q_{3}$
or $Q_{1} - 2 Q_{2} + 4 Q_{3} = 0$
or $Q_{1} - 2 Q_{2} + 4 (Q_{1} - Q_{2}) = 0$
or $5 Q_{1} = 6 Q_{2}$ or $6 Q = 11 Q_{1}$
loop ADEBMA
$C V = Q_{2} + Q_{2} - Q_{3} + Q_{1} = Q + Q_{2} - Q_{3}$
$= Q + Q_{2} - (Q_{1} - Q_{2})$
$= Q + 2 Q_{2} - Q_{1}$
$= 3 Q - 3 Q_{1}$
$= 3 Q - 3 \times \frac{6 Q}{11} = \frac{15}{11} Q$
$C_{e q} = \frac{Q}{V} = \frac{11}{15} C = 22 μ F$

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Some capacitors each of capacitance 30μF are connected as shown in figure. Calculate the equivalent capacitance (in μF) between terminals A and B.

Some capacitors each of capacitance $30 μ F$ are connected as shown in figure. Calculate the equivalent capacitance (in $μ F$ ) between terminals $A$ and $B$ .