What is series combination of capacitors. Derive the formula for equivalent capacitance in series combination.

Explanation

Series combination : If a number of condensers are connected end to end between the fixed points then such combination is called series.
In this combination 1. Charge on each capacitor is equal.
2. P.D's across the capacitors is not equal.
Consider three capacitors of capacitances `C_(1), C_(2)` and `C_(3)` are connected in series across a battery of P.D V as shown in figure.
Let Q be the charge on each capacitor
Let `V_(1), V_(2)` and `V_(3)` be the P.D's of three capacitiors then
`V = V_(1) + V_(2) + V_(3)` -------(1)
P.D across `I^(st)` condenser `V_(1) = (Q)/(C_(1))`
P.D across `II^(nd)` Condenser `V_(2) = (Q)/(C_(2))`
P.D. across `III^(rd)` condenser `V_(3) = (Q)/(C_(3))`
`:.` From the equation (1), `V = V_(1) + V_(2) + V_(3)`
`= (Q)/(C_(1)) + (Q)/(C_(2)) + (Q)/(C_(3)) = Q [(1)/(C_(1)) + (1)/(C_(2)) + (1)/(C_(3))]`
`(V)/(Q) = (1)/(C_(1)) + (1)/(C_(2)) + (1)/(C_(3))`
`(1)/(C) = (1)/(C_(1)) + (1)/(C_(2)) + (1)/(C_(3)) + (1)/(C_(3)) + ...+ (1)/(C_(n))`