# How do I calculate output voltage from a given supply voltage and resistance?

I have searched everywhere but I can't seem to find out how I can calculate the output voltage (or voltage over a component) from the resistance of a resistor (or other component) and the supply voltage. Everything seemed to be about Ohm's Law, which looks like it could help but I don't know how.

In the case I need to solve, there is a supply of 5v and I need to get the resistance needed to lower the voltage for an LED (the current and resistance at optimum voltage I can get if needed) to 3v. I will definitely need to do this operation again so if you could give something like an equation, rather than the necessary resistance.

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Something to do with the internal resistance of the power supply? –  leongz Apr 12 '12 at 17:20

You need to know the resistance of the LED: call this $R_{LED}$ and call the resistor $R$. The current flowing out of the power supply is just the voltage (5 volts) divided by total resistance, $I = V/R$, so:

$$I = \frac {5}{R + R_{LED}}$$

The voltage drop across your resistor, $R$, is just $V = IR$ and you want this to be two volts to leave a three volt drop across the LED, so:

$$2 = IR = \frac {5R}{R + R_{LED}}$$

and a quick rearrangement gives:

$$R = \frac{2}{3}R_{LED}$$

More generally, suppose the power supply voltage is $V$ and the voltage drop across the resistor is $V_R$, then you get:

$$V_R = \frac {VR}{R + R_{LED}}$$

so:

$$R = \frac{V_R}{V - V_R} R_{LED}$$

But as user1631 says, this assumes the LED can be treated as a simple resistor, and in practice this isn't true. A quick Google found http://www.oksolar.com/led/led_color_chart.htm, which gives some graphs of current against voltage for LEDs. In fact the same Google found http://en.wikipedia.org/wiki/LED_circuit, which describes exactly the problem you're asking about.

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