Question

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?

Answer 1

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.

Answer 2

Both the expressions are correct. In the first case, I remain constant whereas the second expression is true when V remains constant

So, the expression P = I2R is used when resistances are connected in series because in series connection the current in each resistance is constant.

Similarly, when resistances are connected in parallel the voltage is constant and so power becomes inversely proportional to R.