Regard as a pair of two identical capacitors. In which situation is the capacitance of the pair greater?

Ans:

The effective capacitance of a couple of capacitors in series Cs is given by

Cs = 1/( 1/C1 + 1/ 1/C2 )

For the case of two capacitors with one as well as the same capacitance C

C1 = C

And

C2 = C

So

Cs = 1/( 1/C + 1/C )

Cs = 1/( 2/C )

Cs = C/2.

The efficient capacitance of a pair of capacitors in parallel, Cp, is given by

Cp = C1 + C2

For the case of two capacitors with one as well as the same capacitance C

C1 = C

And

C2 = C

So

Cp = C + C

Cp = 2C.

Since Cs = C/2 and Cp = 2C we have Cp > Cs. That is to articulate that the capacitance of the pair of identical capacitors is greater when the capacitors are connected in parallel.