The electric power consumed by a
device may be calculated by using either of the two expressions P =

I2R or P = V2/R . The first expression indicates that it
is directly proportional to R where as the second

expression indicates inverse
proportionality. How can the seemingly different dependence of P on R in these

expressions be explained?



I and R are not independed quiantites. If you increase R, I will decrease. If you decrease R, I will increse. You have remeber that relation, and then look at the squares. Remember V=IR 
So in P = V^2/R if R increases the I will decrease if V stays constant 
So in P=I^2R Even though R is increasing I will be decreasing more rapidly because it is squared leading to a drop in power in both equations.