Question

(a) The electric power consumed by a device can be calculated by using either of the two expressions: $\mathrm{P}={\mathrm{I}}^2\mathrm{R}\mathrm{or}\mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}}$. The first expression indicates that it is directly proportional to R, whereas the second expression indicates inverse proportionality. How can the seemingly different dependence of P on R in these expressions be explained?

Answer 1

Dear student
$P=I^{2}R$ 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.

Resistance is the property of material and resistance of a conductor depends upon the nature of its material, such as length of the conductor, cross-sectional are of the conductor, temperature, etc. It does not depends on the power. Electric power is basically a derived quantity, which we derive by using Ohm's law and it is not the basic property. Thus you can not conclude that power is directly or inversely proportional to the resistance. However, electric power of an electric circuit depends on the current and voltage, since it is the function of current flows through it against a potential difference.

Regards