1. The problem statement, all variables and given/known data What must the emf ε in the figure be in order for the current through the 7.00 ohm resistor to be 1.75A? Each emf source has negligible internal resistance. 2. Relevant equations Kirchhoff's Rule: [itex]\sum I=0[/itex] junction rule [itex]\sum V=0[/itex] loop rule 3. The attempt at a solution I have drawn my current directions as shown in the attachment below. By the junction rule, I know that [itex]I_2 = I_3+I_1[/itex] and it is given that [itex]I_2=1.75A[/itex]. I drew a loop clockwise around the entire thing and came up with the following equation: [itex]24V-(7 ohm)(1.75A)-(I_1)(3 ohm) = 0[/itex] so that I have [itex]I_1 = (24V-12.25V)/3= 3.92A[/itex] and then [itex]I_3 = I_2 - I_1 = 2.17[/itex] Drawing loop 2 clockwise within the right inner loop I have the following equation: [itex]-(7 ohm)(I_2) - (I_3)(2 ohm) + ε = 0[/itex] solving for ε, I get [itex]ε = (12.25V)+(4.34V) = 16.59V[/itex] Also, if I draw a clockwise loop inside the right inner loop, I have the following equation: [itex]-ε + (I_3)(2 ohm) - (I_1)(3 ohm) + 24 V = 0[/itex] which simplifies to [itex]ε = 16.58V[/itex] I can find no mistakes (and I have checked over my work a few times) but it is the wrong answer. Could anyone please help me? Thanks!