Question

The power dissipated in a resistor is given by P=V2/R , which means power decreases if resistance increases. Yet this power is also given by P=I2R , which means power increases if resistance increases. Explain why there is no contradiction here.

Answer 1

NEITHER eqn implies anything until you specifi the datafor a given situation. The 1st eqn makes a claim about how the power dissipated by a resistor depends on both its resistance R and te potential difference V across it. The second eqn states that te powee depends on three independednt quantities: V, I and R. However these are also related by Ohm’s law V=IR. So te two given eqns are not independent- they are connected by a third.

In P=V2R, power decreses with increasing R only if V= constant. But Ohms law then predicts that for constant V as the resistance goes up the current muat go down since I=V/R. The power in p=I2R implies that two powers of I decrese while one power of R increases, the net effect being a decrese in power- in agreement with the prediction of P=V2/R after all.