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Under what is the heat produced in an electric circuit: (i) directly proportional (ii) inversely proportional to the resistance of the circuit ?

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(i) Heat produced in the circuit is directly proprotional to the resistance if a constant current is flowing through a circuit, because `H=I^(2)Rt or H prop R`. It is so in series combination of resistors.
(ii) Heat produced in the circuit is inversely proprotional to the resistance if a constant pot. diif. is applied across the circuit, because
`H = V^(2)/R t or H prop 1/R`
It is so in parallel combination of resistors.

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