For a simple LR circuit where a DC supply is connected in series with a resistor and an inductor. How is the graph of Vin vs Vout (across the inductor) is going to look? I think Vout is going to be zero for any value of Vin if the inductance is small. But I am not sure if this is going to change if the inductance is increased. Thanks
Do you have any experience with Laplace transforms or differential equations? That's how you'll find the precise answer. You are correct in that the steady state (not transient!) Vout (I assume you are measuring across the inductor) will always be zero, no matter what the inductance value is. Wikipedia has a good page with graphs that you can look at, and maybe we can answer more detailed questions. http://en.wikipedia.org/wiki/RL_circuit
Remember, too, that although ideally the steady-state DC voltage drop across any inductor will be zero, this is only true for an inductor with zero resistance. Any practical inductor actually has some resistance (although small). So, there will be a (small) voltage drop across a practical inductor.
Check out the AAC book, it covers a lot of this... http://www.allaboutcircuits.com/vol_1/chpt_16/index.html
Thanks I derived the equation of Vout across the inductor using Laplace transform, But how am I suppose to conclude that Vout will be zero for any value of Vin ?
Vout will be zero only for the steady state condition, which is when time goes to infinity. Take the limit of the right side of your equation for t->infinity, and you'll see that the result goes to zero regardless of finite values of R and L.