(20%) Problem 5: Consider the circuit in the figure, with the current directions

Question

(20%) Problem 5: Consider the circuit in the figure, with the current directions defined as shown. There are four resistors in this circuit (R1, R2, R3, and R4) and four batteries with emfs epsilon1 = 15.5 V, epsilon2 = 3.5 V, epsilon3 = 15 V, and epsilon4 = 22.1 V, each with internal resistance given by ri. Randomized Variables epsilon1 = 15.5 V epsilon2 = 3.5 V epsilon3 = 15 V epsilon4 = 22.1 V (a) Calculate the current I2 in amps. (b) Calculate the current I3 in amps. (c) Calculate the current I1 in amps.

Explanation / Answer

Consider the node b,
let the voltage at this node = Vb and voltage at node e is 0 V
then,
I1 = (-Vb+E1)/(R1+R4+r1)
I2 = (Vb+E2)/(R2+r2)
I3 = (Vb+E3-E4)/(R3+r3+r4)
we have at node b, I1=I2+ I3
so (-Vb+15.5)/(35.5) = (Vb+3.5)/(6.25) + (Vb-7.1)/(9.25)
solving Vb = 2.17 V

I1 = (Vb-15.5)/(35.5) = 0.375 A
I2 =(Vb+3.5)/(6.25) = +0.9078 A
I3 = (Vb-7.1)/(9.25) = -0.533 A

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