Let i1 be the branch current though r1 i2 be the branch

Question

Assume the resistance values are R1 = 2,200 Ohm, R2 = 1,200 Ohm, R3 = 4,300 Ohm, and R4 = 5,900 Ohm, and the battery emfs are Epsilon1 = 1.5 V and E2 = 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.)

ε₁ - I₁R₁ - I₃R_{3 = 0}

(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.)

-ε₂ + I₃R₃ - I₂R_{2 = 0}

(c) Apply Kirchhoffs 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