Assume the resistance values are R 1 = 2,600 , R 2 = 1,300 , R 3 = 4,300 , and R

Question

Assume the resistance values are

R1 = 2,600 , R2 = 1,300 , R3 = 4,300 , 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.

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

Explanation / Answer

E1 - I1R1 - I3R3 = 0

E2 + I3R3 - I2R2 = 0

by current law

I3 = I1+I2

E2 + R3I1 + R3I2 - R2I2 = 0

given E1 = 1.5

E2 = 3

R1 = 2600 ohm

R2 = 1300 ohm

R3 = 4300 ohm

1.5 - 2600I1 - 1300I2 = 0 ...(1)

3 + 4300I1 + 4300I2 - 1300R2 = 0 = > 3 + 4300I1 + 3000I2 = 0 ..(2)

by solving 1 nd 2

I1 = 3.8 x 10^-3 A

I2 = 6.45 x 10^-3 A

I3 = 0.01025 A

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