Consider the circuit in the figure, with the current directions defined as shown

Question

Consider the circuit in the figure, with the current directions defined as shown. There are four resistors in this circuit (R_1, R_2, R_3, and R_4) and four batteries with emfs epsilon_1 = 16 V, epsilon_2 = 2.5 V, epsilon_3 = 11 V, and epsilon_4 = 29.2 V, each with internal resistance given by r_i as marked in the figure. Randomized Variables epsilon_1 = 16 V epsilon_2 = 2.5 V epsilon_3 = 11 V epsilon_4 = 29.2 V Calculate the current I_2 in amps. Calculate the current I_3 m amps. Calculate the current I_1 in amps.

Explanation / Answer

4 = 20.2 V

Using kVL (mesh) with i1 on left and i2 on right
i1 voltages:
-16 + 20.5i1 + 6(i1 - i2) - 2.5 + 0.25(i1 - i2) + 15i1 = 0
41.75i1 - 6.25i2 – 18.5 = 0 (i1 loop equation)
i2 voltages:
2.5 + 6.25(i2 - i1) + 8i2 - 11 + 1.25i2 + 29.2 = 0
-6.25i1 + 15.5i2 + 20.7 = 0 (i2 loop equation)

And i1 = i2 + i3

Now there are three unknowns and three equations. Solve for i1, i2 and i3

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