Question
Determine all three branch currents in the circuit below, using the indicated reference directions.
The upper branch follows a → b → c → d → e: R₂ = 2.5 Ω, an 18 V source with its negative terminal at b and positive terminal at c, and internal resistance r₁ = 0.5 Ω. I₂ is referenced from a to e along this branch.
The middle branch joins e to a through R₁ = 6.0 Ω. I₁ is referenced from e to a.
The lower branch follows a → h → g → f → e: a 45 V source with its negative terminal at h and positive terminal at g, internal resistance r₂ = 0.5 Ω, and R₃ = 1.5 Ω. I₃ is referenced from a to e along this branch.
Both a and e are junctions shared by the three branches.
Circuit redrawn from OpenStax College Physics (BCcampus 2016), Section 21.3 Figure 5. The source polarities, values and reference directions are unchanged.
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Evidence boundary
This restates OpenStax College Physics, BCcampus 2016 edition, Section 21.3 Example 1 and Figure 5. The drawing and text preserve its source polarities, all resistances, node labels and current-reference arrows. Results use the ideal steady DC model with the specified internal resistances. The signed solutions are theoretical values under that model, not measurements or a claim of precision beyond the textbook data.