# Electronic – How can Ohms law be used to calculate the resistor value for an LED when multiple voltage/current pairings give the same resistance

circuit-designohms-lawtheory

Say I have a 9V supply, and I want to power an LED that requires 3V and 0.02A. From what I understand, I need to add a resistor that will drop 6V, and reduce the current to 0.02A, and I can calculate the resistance needed using ohms law. So, 6/0.02 = 300Ω – simple enough.

But how can this be the correct resistor when there's plenty of other equivalent fractions that would produce the same result? 3/0.01 also gives 300, so surely you could calculate that this resistor will only drop 3V and reduce the current to 0.01A? What am I missing here?

3/0.01 also gives 300,

This tells you what resistor you'd need if you wanted 10 mA, and you had a supply of $$\V_f + 3\ {\rm V}\$$. Since that isn't your situation, this result is irrelevant to you. Whether it happens to produce the same resistance required as your situation or not.

If you want to drive 30 miles in 30 minutes, you need to drive at 60 miles per hour. Similarly, if you need to drive 120 miles in 120 minutes, you also need to drive 60 miles per hour. Getting the same numerical result for the 2nd problem doesn't invalidate the solution to the first problem.