Discuss capacitors in series and in parallel.

CAPACITORS IN SERIES

The circuit in which all the capacitors are connected one after another in the same path so that the same charge or current flows to each capacitor is called capacitor in series.

Consider three capacitors \(C_1\), \(C_2\) and \(C_3\) are connected in series with battery of potential difference \(V\). The Kirchhoff's second rule gives $$ V=\ V_1+V_2+V_3 $$ The charge \(Q\) of capacitors connected in series is common to all capacitors. The equivalent capacitance \(C_{eq}\) of three capacitors connected in series is $$ \frac{Q}{C_{eq}}=\ \frac{Q}{C_1}+\frac{Q}{C_2}+\frac{Q}{C_3} $$ $$ \frac{1}{C_{eq}}=\ \frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3} $$ For \(n\) capacitors connected in series, the reciprocal of equivalent capacitance \(C_{eq}\) is equal to the sum of the reciprocals of capacitances of the individual capacitors. $$ \frac{1}{C_{eq}}=\ \sum_{i=1}^{n}\frac{1}{C_i} $$ Where \(i=1,\ 2,\ 3,\ 4,\ \ldots.,\ n\)

CAPACITORS IN PARALLEL

The circuit in which all the capacitors are connected side by side in different paths what the same charge or current will not flow through each capacitor is called parallel capacitor circuit.

Consider three capacitors \(C_1\), \(C_2\) and \(C_3\) are connected in parallel with battery of potential difference \(V\).

When a voltage is applied to the parallel circuit, each capacitor will be different charge. The capacitor with high capacitance will get more charge where capacitor with less capacitance will get less charge. The total charge \(Q\) is given as $$ Q=\ Q_1+Q_2+Q_3 $$ $$ C_{eq}V=\ C_1V+C_2V+C_3V $$ $$ C_{eq}=\ C_1+C_2+C_3 $$ The equivalent capacitance \(C_{eq}\) is equal to the sum of the capacitances of the individual capacitors when \(n\) capacitors are connected in parallel. Where \(i=1,\ 2,\ 3,\ 4,\ \ldots.,\ n\)