Use Kirchhoff’s rules to analyze the circuit in Figure P19.56.
(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.
(b) Write Kirchhoff’s loop rule relation for a loop that travels through battery 2, resistor 2, and resistor 3.
(c) Apply Kirchhoff’s junction rule to the junction at A to get a relation between the three branch currents.
(d) You should now have three equations and three unknowns (I₁, I₂, and I₃). Solve for the three branch currents.

R₁ = 2400 V, R₂ = 1400 V, R₃ = 4500 Ω, and R₄ = 6000 Ω, and the battery emfs are ε₁ = 5 1.5 V and ε₂ = 5 3.0 V, unless stated otherwise

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R2 R1 E2 R3 Figure P19.56