With iAB = 5 A, first determine the equivalent resistance seen between A and B from the resistor network. The network reduction gives approximately 6.842 Ω, so VAB = iAB Req ≈ 5 × 6.842 = 34.21 V.
Formula / Key Relation
VAB = iAB Req
Req ≈ 6.842 Ω
VAB ≈ 5 × 6.842
≈ 34.21 V
Detailed Explanation
Concept & ReasoningThis is a pure resistive-network question, so VAB is obtained from the equivalent resistance between terminals A and B. The vertical 5 Ω and 10 Ω resistors prevent treating the two outer paths as simple independent series branches; the network must be reduced using node-voltage/bridge transformation or solved by applying a test voltage/current. If a 1 V test source is applied across A-B and the resulting input current is calculated from nodal equations, Req is obtained as Vtest/Itest. Scaling to the specified 5 A terminal current then gives the terminal voltage. The official answer corresponds to Req ≈…
Concept & Reasoning
This is a pure resistive-network question, so VAB is obtained from the equivalent resistance between terminals A and B. The vertical 5 Ω and 10 Ω resistors prevent treating the two outer paths as simple independent series branches; the network must be reduced using node-voltage/bridge transformation or solved by applying a test voltage/current. If a 1 V test source is applied across A-B and the resulting input current is calculated from nodal equations, Req is obtained as Vtest/Itest. Scaling to the specified 5 A terminal current then gives the terminal voltage. The official answer corresponds to Req ≈ 6.842 Ω and hence 34.21 V.
How to Solve It in the Exam
For a complicated passive network, apply a 1-V test source and solve nodal voltages; the input current immediately gives Req.
Important Exam Point
Do not combine resistors as series/parallel when their common node has another branch attached.
Related Revision Path
This question sits in the revision path Network Theory → Resistive Networks → Bridge/Network Reduction .
Quick Trick
For a complicated passive network, apply a 1-V test source and solve nodal voltages; the input current immediately gives Req.
Common Mistake
A bridge-looking network is not automatically balanced; verify balance conditions before removing the cross branch.
Exam Tip
Do not combine resistors as series/parallel when their common node has another branch attached.
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