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Make sure that the current distribution over two resistances R1 and R2 connected in parallel corresponds

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Make sure that the current distribution over two resistances R1 and R2 connected in parallel corresponds to the minimum thermal power generated in this circuit.

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We assume current conservation but not Kirchhoff's second law. Then thermal power dissipated is

The resistances being positive we see that the power dissipated is minimum when

This corresponds to usual distribution of currents over resistance joined is parallel.

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