Two capacitors with capacitances `C_(1) and C_(2)` are connected in parallel. Find the resultant capacitance.

Explanation

When the capacitors are connected in parallel (Fig. 24.9), all their interconnected plates have the same potential, therefore `q_(1)=C_(1)( varphi_(1)-varphi_(2)) and q_(2)=C_(2)(varphi_(1)-varphi_(2))`, where `q_(1) and q_(2)` are the charges of the respective capacitors. The charge of the system is
`q=q_(1)+q_(2)=(C_(1)+C_(2)) (varphi_(1)-varphi_(2))`.
On the other h and `q=C(varphi_(1)-varphi_(2))`, where C is the equivalent capacitance. Hence the formula sought.