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Two conducting wires of the same material and of equal length and equal diameters are first connected in series and then in parallel in a circuit. Find the ratio of heat produced in series and parallel combination. Note:- *the question doesn't say across the same potential difference*
Asked by anoushkakhemani | 31 Oct, 2020, 06:04: PM
If each wire has resistance R, when they are connected in series, equivalent resistance is 2R

When connected in parallel, equivalent resistance is ( R/2)

Case-1

If the wires are connected across constant potential difference , then power P =(  V2 / Resistance )

Power dissipated in Series resistors , P1 = V2 / (2R)

Power dissipated in parallel resistors , P2 = (2V2 ) / R

Hence ratio of power dissipation = ( P1 / P2 )  = 1/4

Case-2

If constant current I is passed through wires , the power  P = I2 × Resistance

Power dissipated in Series resistors , P1 =  I2 (2R)

Power dissipated in parallel resistors , P2 = I2 ( R / 2 )

Hence ratio of power dissipation = ( P1 / P2 )  =  4
Answered by Thiyagarajan K | 31 Oct, 2020, 07:22: PM

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