Vout = Vin x R2 / (R1 + R2) If Vin is 12V and I want Vout to be 4.5V What would the equation/math be to find the values for R2 and/or R1 if given. If R1 is given R2 would be a common factor?
There is no unique solution. There must be some other condition. For example R1 + R2 must be 20K Ohms. Now there is a unique solution because you have two equations and two unknowns.
Et = 12v you need to know the current. so use .1 amp arbitrarily. It = .1amp find R1 and R2 by using Rt = Et/It or 12v/.1amps = 120ohms total resistance if you want 4.5 volts then R1 = 4.5v-12v = 7.5v drop 7.5v / .1amps = 75 ohms = R1 4.5v / .1amps = 45ohms = R2 the same curent flows through both resistors. so that is used to find the total resistance and ratio is used to find voltage drops and resistances are in proportion to current.