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.