Question

Two capacitors of capacitance C₁ and C₂ are connected in parallel and this combination is connected in series with a capacitor of capacity C₃. Calculate the equivalent capacity of the combination of capacitors.

Answer 1

As per given condition, circuit diagram is

Case I: C₁ and C₂ are connected in parallel.

C_P = C₁  + C₂

Case II: This combination is connected in series with C₃ i.e. C_P is connected in series with C₃.

∴ Circuit will be as shown below:

∴ `1/C_s = 1/C_P + 1/C_3`

∴ `1/C_s = (C_P + C_3)/(C_P  C_3)`

∴ `C_(eq) = C_s = (C_P  C_3)/(C_P + C_3)` 

= `((C_1 + C_2)C_3)/(C_1 + C_2 + C_3)`

= `(C_1  C_3 + C_2  C_3)/(C_1 + C_2 + C_3)`