Question

Obtain an expression for equivalent capacitance when three capacitors C₁, C₂ and C₃ are connected in series.

Answer 1

All the capacitors are connected in series, In the fig. are shown three capacitors of capacity C₁, C₂, C₃ connected in series. The charge Q flowing through each of the capacitors is the same but potential difference across them will be different. If V₁, V_2, and V₃ are the potential difference across them, then

`"V"_1 = "Q"/"C"_1 , "V"_2 = "Q"/"C"_2 , "V"_3= "Q"/"C"_3`

If C is the capacitance of the combination, then

V = `"Q"/"C"`

Also, V = V₁ + V₂ + V₃

or `"Q"/"C" = "Q"/"C"_1 + "Q"/"C"_2 + "Q"/"C"_3`

`1/"C" = 1/"C"_1 +1/"C"_2 + 1/"C"_3` , which is the required relation.