Cells connected in Series

 Cells connected in Series

 

1) Two cells are connected in series means, negative electrode of one cell is connected to the positive electrode of the second cell, as shown in the diagram below:

 

2) The two cells have emf e₁ &  e₂  with internal resistance r₁ & r₂ respectively.

3) Now when these cells are in a closed circuit, current starts flowing, say I amount of current is flowing.

4) Now potential difference across A & B position is

V_AB = e₁ – Ir₁

5) Now potential difference across B & C position is

V_BC = e₂ – Ir₂

6) Now potential difference between A & C is

V  =  V_AB   +   V_BC

V  =  ( e₁ – Ir₁ )  +  ( e₂ – Ir₂ )

 

V  = (e₁ + e₂)  –  I(r₁  +  r₂)   ………  3.48

7) Now if these cells is like a single cell of emf  (eeq)  & internal resistance r_eq  then

V  = eeq – Ireq         ………  3.28

 

Comparing 3.48  &   3.28

eeq  =  e₁  + e₂

&

req  =  r₁  +  r₂