Now, we apply Kirchhoff's loop rule in loop 1 and loop 2 to get following equations: In loop 1 0. −iR−(i+i1)R−2E+E=0 or −2iR−i1R=E or i1R+2iR=−E...(i) In loop 2 −3E+i1R+
i1
2
R+i1R+2E+(i+i1)R=0 or
7
2
i1R+iR=E or 7i1R+2iR=2E(ii) Now 7×Eq.(i)−Eq.(ii) gives : 7i1R+14iR=−7E 7i1R+2iR=2E ⇒12iR=−9E ⇒i=