The current i in the circuit given below is

Step-by-step solution

Lets assume current distribution in given circuit is as shown Now, we apply Kirchhoff's loop rule in loop 1 and loop 2 to get following equations: In loop 1, -i R- (i+i₁ ) R-2 E+E=0 or -2 i R-i₁ R=E or i₁ R+2 i R=-E ...(i) And in loop 2, -3 E+i₁ R+ i₁ 2 R+i₁ R+2 E+ (i+i₁ ) R=0 or 7 2 i₁ R+i R=E or 7 i₁ R+2 i R=2 E ...(ii) Now 7 eq. (i)-eq. (ii) gives 12 i R=-9 E i= -9 E 12 R i= -3 E 4 R