Find the emf and internal resistance of a single battery which is equivalent to a combination of three batteries as show in figure.

Explanation

The given combination consists of two batteries in parallel and resultant of these two in series with the third one.
For parallel combination we can apply.
`E_(eq)=(E_1/r_1-E_2/r_2)/(1/r_1+1/r_2)=(10/2-4/2)/(1/2+1/2)=3V`
Further, `1/r_(eq)=1/r_1=1/r_2=1/2+1/2=1`
`= :. r_(eq)=1Omega`
Now this is in series with find one i.e.

The equivalent emf of these two is `(6-30 Vor 3V)` and the internal resistance will be `(11)` or `2Omega`