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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 power dissipated in the resistor 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
We have two relations
P=i2Rand P=V2R. This causes confusion. But this is how you solve such a problem.
If R increases, 'i' would clearly decrease because V=iR
Thus in the first equation, i and R are both variables.
In the second equation, V wouldn’t change since the battery keeps it constant.
That means we have to use P=V2R. In other words, use the equation where one quantity i constant.
ThusPα1R and hence
Power delivered will decrease.

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