By the way the device draws 1 amp.
This was the critical piece of information missing from your original question. With it, this question can be easily answered. Even so, there is one further important detail that must be clarified - that this 1 amp will be
constant.
Ohm's Law will give you the answer. The formula is V = IR Volts = Current x Resistance **
So, since the Voltage will be the voltage across the Resistor, V = 18.2 - 15 which is 3.2V
The formula now looks like this: 3.2 = 1 x R
R is obviously 3.2 ohms
If you want to get the generic formula for working out the resistance, then you just apply a little algebra. Take V = IR and divide both sides by 'I'. this gives you V/I = R. Plug in the numbers above and R = 3.2/1 ... same answer!
Now we know the resistance, we have to make sure we get one that can withstand the power it will need to handle. This is done using another formula - which is just as simple as the one above....
P = VI where P is the power (in Watts) with V and I being the same as we have just used.
Substituting for V and I (plugging in the actual numbers) we get:
Power = 3.2 x 1 which is 3.2 Watts
What does this mean? dissipation rating of Vz x Iload
We just worked it out. Dissipation just means 'the amount of power that has to be got rid of'.
So, you will need a resistor with a value of 3.2 ohms and a power rating of at least 3.2 watts. The resistance value needs to be 3.2 ohms (or close enough) for the voltage drop to be correct, but its power rating can be more. Choose a resistor with a lower power rating and it is going to heat up far too much and it will fail.
** You can blame the French for 'I' representing Current - but don't get too worked up about it ... between Current and Capacitance, one of them had to lose out.
Also, just to add confusion, 'E' or 'U' can sometimes be used for Voltage.