Find the potential difference across each cell and the rate of energy dissipated in `R`

Answer

` (48)/(7)V`, (48)/(7)V,11.75W`

Explanation

Appliying kirchhoff's loop law we get

For loop `ABEFA`
`4(I+ I_(1)) + 2I = 12 or 6 l + 4I_(1) = 12` ……(i)
For loop `BEDCFB`
`4(I+ I_(1)) = or 4 I + 5I_(1) =6`……(ii)
Solving (i) and (ii) we get
`I = (18)/(7) A and I_(2) = - (6)/(7)A`
Pot diff across R
`V = (I + I_(1)) R = ((18)/(7) - (6)/(7)) xx 4 = (48)/(7) V`
Pot diff across each cell = pot diff across `R`
`= (48)/(7)V`
Rate of energy disspated in `R = (I + I_(1))^(2) R`
`= ((18)/(7) - (6)/(7))^(2) xx 4 W = ((12)/(7))^(2) xx 4 = 11.75 W`