Assume the resistance values are R1 = 2,200 Ohm, R2 = 1,300 Ohm, R3 = 4,200 Ohm,

Question

Assume the resistance values are R1 = 2,200 Ohm, R2 = 1,300 Ohm, R3 = 4,200 Ohm, and R4 = 5,900 Ohm, and the battery emfs are epsilon1 = 1.5 V and Epsilon2 = 3.0 V. Use Kirchhoff?s rules to analyze the circuit in the figure below. (a) Let I1 be the branch current though R1, I2 be the branch current through R2, and I3 be the branch current through R3. Write Kirchhoff?s loop rule relation for a loop that travels through battery 1, resistor 1, and resistor 3. (Use a clockwise current loop when entering your answer. Use any variable or symbol stated above as necessary.) Epsilon1+I1R1-I3R3 =0 (b) Write Kirchhoff?s loop rule relation for a loop that travels through battery 2, resistor 2, and resistor 3. (Use a clockwise current loop when entering your answer. Use any variable or symbol stated above as necessary.) -Epsilon2+I3R3-I3R3 =0 (c) Apply Kirchhoff?s junction rule to the junction at A to get a relation between the three branch currents. (Use any variable or symbol stated above as necessary.) I1= I2+I3 (d) You should now have three equations and three unknowns (I1, I2, and I3). Solve for the three branch currents. I1 = A I2= A I3= A

Explanation / Answer

a)

Here , Using KVL

E1 - I1 *R1 - I3*R3 = 0

b)

E2 +R2*I2 - I3*R3 = 0

c)

I1 = I2 + I3

d)

solving these equation by using values given

I1 = -2.48 *10^-4 A

I2 = -7.35 *10^-4 A

I3 = 4.87 *10^-4 A

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