Resistors R1, R2, R3, and R4 are arranged in a circuit as shown in the figure ab

Question

Resistors R1, R2, R3, and R4 are arranged in a circuit as shown in the figure above. The direction of positive currents I1, I2, I3, and I4 through the resistors are shown. (i.e., negative current values correspond to currents in the opposite direction to that shown above). The values for the resistors and the batteries in the circuit are: R1 = 100 ?, R2 = 200 ?, R3 = 30 ?, R4 = 400 ?, V1 = 4 V, and V2 = 12 V.

What is the value of I2, the current through R2? (remember I2 is a signed number) I2 = ?

Explanation / Answer

using KVL to the left loop

-(i1*R1)-(i3*R3)+V1 = 0

(100*i1)+(30*i3) = 4..................(1)

apply KVL to the middle loop

-(i2*R2)+V2+(i3*R3) = 0

-(i2*200)+12+(i3*30) = 0

200*i2 - 30*i3 = 12..............(2)

and also i1 = i2 + i3

i1-i2-i3 = 0 ............(3)

Apply KVL to the right loop

-(i4*R4)-V2 = 0

i4 = -12/400 = -0.03 A

Solving (1),(2) and (3) we get

i1 = 0.04413 A

i2 = 0.05793 A

and i3 = -0.01379 A

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.