Question

The electric power consumed by a device may be calculated using either of the 2 expressions :P = I²R or P = V²/R .The first expression indicates the power is directly propotional to R, whereas the second expression indicates inverse propotionality.

How can seemingly different dependence of P on R in these expressions be explained?

Answer 1

$P=I^{2}R$ and $P=\frac{V^2}{R}$ are basically the same relation. First one is usually used when I is constant and second one when V is constant.
Using $I=\frac{V}{R}$ one can be derived from the other.
$P=I^{2}R={\left(\frac{V}{R}\right)}^{2}R=V^{2}R$
In case of parallel circuits when V is constant we use V²/R.But in case of series circuit when I is constant we use I²R.