Assume the resistance values are R1-2, 300 , R2 = 1,500 , R3 = 4,600 , and R4-6,

Question

Assume the resistance values are R1-2, 300 , R2 = 1,500 , R3 = 4,600 , and R4-6,200 , and the battery emfs are 1 1.5 v and ,-3.0 V Use Kirchhoff's rules to analyze the circuit in the figure below (a) Let I1 be the branch current though R1, 12 be the branch current through R2, and 13 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.) (b) Write Kirchhoffs 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.) -28 (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.) (d) You should now have three equations and three unknowns (I1, I2, and I3). Solve for the three branch currents.

Explanation / Answer

Great job in solving the first three. The last one is just solving the above 3 linear equations to get the unknowns.

I1 = I2 + I3 ---(1)
E1 = I1R1 + I3R3 ----(2)
E2 = I3R3 - I2R2 ----(3)

Substituting eqn 1 in eqn 2
E1 = I2R1 + I3(R1 + R3)
1.5 = 2300 I2 + I3(6900)---(4)

Eqn 3 after substituting the values is
3 = 4600 I3 - 1500 I2

I2 = -6.58 x 10-4 A
I3 = 4.371 x 10 -4 A

I1 = I2 + I3 = -2.209 x 10-4 A ( the directions you assumed is wrong, hence the negative signs)

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