We know that in the series combination current will be same across all the capacitors and voltage gets divided across themi = c dv/dt => V = ∫ (i/c) dt
v = v₁ + v₂ + v₃
∫ (ieq/ceq) dt = ∫ (i₁/c₁) dt + ∫ (i₂/c₂) dt + … + ∫ (in/cn) dt
i = i₁ = i₂ = in
∫ (i/ceq) dt = ∫ (i/c₁) dt + ∫ (i/c₂) dt + … + ∫ (i/cn) dt
i/ceq = i/c₁ + i/c₂ + … + i/cn
Ceq = 1/ (1/c₁ + 1/c₂ + 1/cn)
In the parallel combination voltage will be same across all the capacitors and current gets divided across all the capacitorsi = i₁ + i₂ + i₃
i = c dv/dt
ceq dv/dt = c₁ dv₁/dt + c₂ dv₂/dt + … + cn d vn /dt
v = v₁ = v₂ = … = vn
ceq dv/dt = c₁ dv/dt + c₂ dv/dt + … + cn dv/dt
ceq = c₁ + c₂ + … + cn