How Do You Calculate the Correct Resistor Values for a Simple Voltage Regulator?

[bengaltiger14]

I am to design a simple voltage regulator(resistors only) to deliver 7.00 volts to a load with a 10v power supply. The circuit will be 1 resistor in series with two parallel resistors. The last parallel resistor being Rload (which can vary from 1000 to 1500 ohms).

Through experiment, I found that I could use a 100 ohm resistor for R2 which would make R1 a 40 ohm resistor. My problem is determining the value for R1 through calculation.

R2 and Rload at 1000 ohms is 91 ohms. So I use the formula: (91/(91+R1)) * 10 = 7.0. Is the right in determing R1? If you plug 40 for R1 is works.

I just need calculations proving this and I think I am having algebra problems solving for R1.

 

[Lambduh]

I think the easiest way to do this is just pick a value for Rload and set R2 to the same value. So their resistance is effectively half of one of their values. For simplicity i chose 1k ohms.

Then since you know you want the value across them to be 7 volts use ohms law to solve for the current. I = V / R. I = 7v / 500 ohms this gives 14mA.

To solve for the value of the first resistor use ohms law again in the form of R = V / I. We can do this because we know the current flowing through the series circuit and we know we want 3V across the first resistor.

R = 3V/ 14mA, R = 214 ohms.