Two identical cells either in series or in parallel combination , gives the same current of 0.5 A through external resistance of `4Omega`. Find emf and internal resistance of each cell.

Explanation

Let each cell be of emf E and internal resistance r, `R=4Omega`, I=0.5 A
When the two cells are connected in series :
Total emf =E+E=2E , Total resistance = 4+r+r
=4+2r
`therefore` Circuit current
`I=E/(R+r)`
`therefore I_1=(2E)/(4+2r) to ` (1)
When the two cells are connected in parallel :
Total emf =E , Total resistance =`4+r/2`
Circuit current `I_2=E/(4+r/2) =(2E)/(8+r) to` (2)
As `I_1=I_2`
8+r=4+2r
4=r
`r=4Omega`
eqn. (1) `rArr` 0.5 =`(2E)/(4+2(4)) rArr 2+4=2E rArr 6/2 =E rArr E=3V`