Cells connected in Parallel

 Cells connected in

Parallel

 

1) Suppose two cells are connected parallelly with their cell emf e₁  & e₂  and their internal resistance r₁  &  r₂ respectively.

 

2) Suppose I₁ current is flowing through the cell e₁ 

3) And I₂ current is flowing through the cell e₂ 

4) then the total current I flowing across A & B is

I  =  I₁  +  I₂  

 

5) Since both cells are connected in same manner and hence the potential across the two cells are same. Say this potential is V.

For first cell,

V = e₁ – Ir₁

 

Similarly for second cell

V = e₂ – Ir₂

 

 

 

6) Now we know that

I  =  I₁  +  I₂  

Therefore

 

 

 

7) Now suppose  (eeq) is the resultant emf of the two cells & r_eq  is the resultant resistance of these two cells, then

V  = eeq – Ireq         ……… 3.47

 

10) Now comparing 3.26  &  3.47

 

 

Now

 

Again

 

 

Now suppose there have n cell with emf e₁, e₂, e₃, ………. e_n and their internal resistance r₁, r₂, r₃, …… r_n    respectively and they are connected parallelly