Some Thoughts on 1/4 Watt Resistors

Today we visit power and how it affects the limits of voltage we work with when building circuits with the standard 1/4 watt resistor:

How much voltage can I put across a 1/4 watt resistor and not exceed its power rating?

Power, P = I*E

But I don't know I and I want to know E...

E = P/I

What does I equal?

Well, with Ohm's Law, I know that I = E/R, and I can substitute!

So...E = P/(E/R)  which, when re-arranged gets; E = P*R/E

Multiplying both sides by E:

E² = P*R

Since we are looking for E, we take the square root of both sides:

E = SquareRoot(P*R)

When we plug ressitance values for up to 5KΩ resistors, we get the graph above.