Assume the resistance values are R 1 = 2,600 ?, R 2 = 1,300 ?, R 3 = 4,200 ?, an

Question

Assume the resistance values are

R1 = 2,600 ?, R2 = 1,300 ?, R3 = 4,200 ?, and R4 = 6,100 ?,

and the battery emfs are

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.)
= 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.)
  = 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 =  

(d) You should now have three equations and three unknowns (I1, I2, and I3). Solve for the three branch currents.

Explanation / Answer

a)

I1 R1 + I3 R3 - E1 = 0

2600 I1 + 4200 I3 - 1.5= 0                    Eq-1

b)

I2 R2 + E2 - I3 R3 = 0

1300 I2 + 3 - 4200 I3 = 0                eq-2

c)

I1 = I2 + I3                           eq-3

Using eq-1 and eq-3

2600 (I2 + I3  ) + 4200 I3 - 1.5= 0  

2600 I2 + 6800 I3 - 1.5 = 0            eq-4

Using eq-2 and eq-4

2600 I2 + 6800 ((1300 I2 + 3)/4200) - 1.5 = 0

I2 = - 0.000714 A

Using eq-4

2600 (- 0.000714) + 6800 I3 - 1.5 = 0

I3 = 0.000494 A

Using eq-3

I1 = I2 + I3 = - 0.000714 + 0.000494 = - 0.00022 A

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