Capacitors connected parallelly

 Capacitors connected parallelly

 

1) Now suppose 3 capacitors C₁, C₂ & C₃ are connected parallelly with a battery

2) Now V potential is applied to these capacitors.

3) As capacitors have different capacitance, So net charge developed on each capacitors will also be different.

4) Say Q₁, Q₂ & Q₃ be the charges developed on each capacitors.

5) Now the total charge in the system is

Q _total = Q₁ + Q₂  + Q₃

 

6) but we know that

Q₁ = VC₁

Q₂ = VC₂

Q₃ = VC₃

7) therefore we get that

Q _total = Q₁ + Q₂  + Q₃

Q _total = VC₁ + VC₂ + VC₃     ….……… 2.36

8) Suppose the resultant net capacitance of the system is C_net then,

Q _total = VC _net    

now putting the value of Q _total from 2.36

VC _net   = VC₁ + VC₂ + VC₃    

We finally get

C _net   =  C₁   +   C₂  +  C₃    

9) Now if there are n no of capacitors with capacitance  C₁, C_2, C_3, C_4, ………… C_n   then

C _net   =  C₁   +   C₂  +  C₃  + ……… + C_n