Find the equivalent capacitance of the system shown in figure between the points a and b.

Explanation

suppose, the capacitor `
`C_3`
` is removed from the given system and a battery is connected between a and b. The remaining system is shown in figure . From the symmetry of the figure, the potential at c will be the same as the potential at d. Thus, if the capacitor `
`C_3`
` is connected between c and d, it will have no charge. The charges of all the remaining four capacitors will remain unchanged. Thus, the system of capacitors in figure is equivalent to that in the figure. The equivalent capacitance of the system in figure can be calculated by applying the formulae for series and parallel combinations. `
`C_1`
` and `
`C_2`
` are connected in series. Their equivalent capacitance is `
` C = (C_1 C_2)/(C_1+C_2)`
`. Two such capacitors are joined in parallel. So the equivalent capacitance of the given system is `
`2C = (2 C_1 C_2)/(C_1 +C_2).