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Question

A resistor of resistance R is connected to an ideal battery (battery with zero internal resistance). If the value of R is increased, the heat developed in the resistor for equal interval of time will ___.

A
increase
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B
decrease
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C
remains unchanged
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D
Data insufficient
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Solution

The correct option is B decrease
Let’s go through this!
Heat dissipated H=i2Rt where the symbols have their usual meanings. Now if the resistance increases, the heat dissipated must increase. Right? Well! NO! That’s not right...
Why?
Here a battery is put across the resistor which maintains a constant potential difference across the resistor. On increasing resistance current (i) will decrease !!!! So the equation H = i^2 Rt is not the right equation to judge the variation (as other variable current also has dependency on resistance)
Let’s write this equation in other form
we know V= iR
so H=i2Rt=v2tR
In this equation V and t are constants, and H, thus varies only with R.
See here, as R increases H decreases…

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