Question

Obtain an expression for the equivalent capacitance of two capacitors C₁ and C₂ connected in series.

Answer 1

capacitors in series

1. The second plate of the first conductor is connected to the first plate of the second conductor, and so on, in a series arrangement.
2. Charges on the plates (Q) are the same on each capacitor in a series combination.
3. The potential difference across the series combination of the capacitor is V volt,
   Where, V = V₁ + V₂
   ∴ V = `"Q"/"C"_1 + "Q"/"C"_2` ...........`("V" = "Q"/"C")`
   Let C_s represent the equivalent capacitance.
   ∴ `"Q"/"C"_"s" = "Q"/"C"_1 + "Q"/"C"_2` ...........`("V" = "Q"/"C")`
   ∴ `1/"C"_"s" = 1/"C"_1 + 1/"C"_2`
   ∴ `"C"_"s" = ("C"_1."C"_2)/("C"_1 + "C"_2)`

The needed expression for equivalent capacitance for a pair of capacitors linked in series is given by the equation above.