power-resistance contradiction

The expressions are meant for calculational purposes and are equivalent. They are connected by Ohm's Law and are not independent. Hence to draw a conclusion of power dependence on R is a bit confusing.

Let's find the answer by a simple experiment.

Pick a battery of potential 10V, we'll connect it across a resistor of 10 Ω.

The current will be 1 A. and Power = VI = 10 W = V²/R = 100/10 = 10 W = I²R = (1²)(10) = 10 W

Now if we want to see how the power is affect as we change the resistance, we have to keep increasing or decreasing the resistance, with contant potential.

Let's increase the resistance to 20 Ω.

V = 10 V, I = 0.5 A and Power = VI = 5 W = I²R = (0.5²)(20) = 5 W = V²/R = 100/20 = 5 W.

So as we keep on increasing the R value we find the power is decreasing. And since the two equations, P = V²/R = I²R are equivalent, but not independent, they are related by Ohm's Law.

Regards,

Team,

TopperLearning.