Three resistances R1 = 5 Ohm, R2 = 1 Ohm and R3 = 3 Ohm, as well as a current source with EMF

Three resistances R1 = 5 Ohm, R2 = 1 Ohm and R3 = 3 Ohm, as well as a current source with EMF ε1 = 1.4 V are connected, as shown in the figure. Determine the EMF ε of the current source, which must be connected in a circle between points A and B, so that a current of I = 1 A flows through the resistance R3 in the direction indicated by the arrow. Disregard the internal supports of the current sources.

Given:
R1 = 5 ohms;
R2 = 1 Ohm;
R3 = 3 ohms;
E1 = 1.4V;
I = 1 A
E =?
We write down expressions of Kirgh’s laws according to the schemes, taking into account that the direction of the contour is clockwise:
For the first circuit:
E1 – I1R1 – I2R2;
For the second circuit:
E + I2R2-R3I;
Sum of currents:
I1 = I2 + I.
The result is a system of equations:
E1 – I1R1 – I2R2 = 0;
E + I2R2 – R3I = 0;
I1 = I2 + I.
Let’s put down the known numerical values:
1.4 – 5I1 – I2 = 0;
E + I2 – 3 = 0;
I1 = I2 + 1.
Substitute I1 in the first expression:
1.4 – 5I2 – 5 – I2 = 0;
E = -I2 + 3.
Find I2 from the first expression:
I2 = – 3.6 / 6 = -0.6 A.
Now we find the EMF:
E = – (- 0.6) + 3 = 3.6 in.
Answer: 3.6 V.