Joule Heating And Energy

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Current passes through a 20 ohm resistor at 2 amperes for 5 minutes in a demonstration, so how much heat energy is produced in the resistor?

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Joule's law of heating states that the heat produced in a resistor equals $H = I^2 R t$, where the power dissipated is $I^2 R$ and $t$ is the time, a result established in NCERT Class 12, Chapter 3 (Current Electricity). First convert the time to seconds: $t = 5 	ext{ minutes} = 300$ s. The power dissipated is $I^2 R = 2^2 	imes 20 = 4 	imes 20 = 80$ W. Multiplying by time gives $H = 80 	imes 300 = 24000$ J. The option 400 J results from carelessly using $t = 5$ s instead of converting the five minutes into 300 seconds. The option 8000 J mistakenly uses $I 	imes R 	imes t$ without squaring the current, dropping a crucial factor of the current. The option 1200 J comes from omitting the resistance term altogether and computing only a partial product of current and time. A plausibility check confirms the magnitude: a resistor steadily dissipating 80 W for five full minutes should release on the order of tens of kilojoules, and 24000 J sits comfortably in that range, while the dimensions of joules equalling watts times seconds are entirely sound, so the result is trustworthy in both size and units.

Joule Heating And Energy

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