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For the network of cells and resistors shown, what is the magnitude and direction of the current flowing through the 1 ohm resistor connected between nodes P and Q?

1. 0.13 A, directed from Q to P
2. 0.13 A, directed from P to Q
3. 1.3 A, directed from P to Q
4. 0 A

Correct answer: 0.13 A, directed from Q to P

Solution

This is a two-loop network where the 1 ohm resistor sits in the middle branch shared by both loops. Using Kirchhoff's rules, the unbalanced emf drives a small current through the central branch. Solving the loop equations gives a current of magnitude 0.13 A, and the sign of the result shows it flows from node Q to node P. The small value (not 1.3 A) and the non-zero result (not a balanced/zero case) confirm option 1.

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