Two cells of emf `E_1.E_2` and internal resistance `r_1 , r_2` respectively are connected to parallel combination. Determine the equivalent emf of the combination.

Explanation

If the equivalent emf of the combination is `F_0` and its equivalent internal resistance is `r_0` then from the figure 1.105,
`r_.=(r_1r_2)/(r_1+r_2),l_1=E_1/r_1,l_2=E_2/r_2andl=E_0/r_0`

`becausel=l_1+l_2,thereforeE_0/r_0=E_1/r_1+E_2/r_2`
or,`E_0=E_1r_0/r_1+E_2r_0/r_2=E_1r_2/(r_1+r_2)+E_2r_1/(r_1+r_2)`
`=1/(r_1+r_2)(E_1r_2+E_2r_1)`