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Question
Obtain an expression for equivalent capacitance when three capacitors C1, C2 and C3 are connected in series.
Solution
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, V2, 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.
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