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
• B. decrease
• C. remains unchanged
• D. Data insufficient

Answer 1

The correct option is B decrease

We have two relations
$P=i^{2}RandP=\frac{V^2}{R}$. 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 $P=\frac{V^2}{R}$. In other words, use the equation where one quantity i constant.
Thus$P\alpha \frac{1}{R}$ and hence
Power delivered will decrease.