Finding R1 and R2 in a Voltage Divider Circuit

[jdawg]

Homework Statement

Consider the voltage divider circuit below. The output voltage is with V₀ =20v with R_L removed ( R_L= ∞Ω) from the circuit. With R_L in the circuit and R_L=380Ω , the output voltage is V ₀=19.192 v . Determine values for R₁ and R₂. I attached a picture of the circuit.

Homework Equations

The Attempt at a Solution

For R_L=∞Ω
20=100((R₁)/(R₁+R₂))

For R_L=380Ω
19.192=(100)((380//R₂)/(380//R₂)+R₁))

Am I on the right track with this? I tried to make a substitution by solving for R1, but it came out really messed up.
Is there a better way to work this problem?

Here is the answer: R1=80Ω R2=20Ω

 

[gneill]

Your approach looks fine, but check your voltage divider equation for the unloaded circuit. The output is across R2, right?

 

[jdawg]

Ohh ok! I fixed my unloaded circuit equation and came up with R₁=4R₂

I think something might be wrong with my R_L=380Ω equation though. I substituted R₁=4R₂ and wound up with -497.56. I've redone my algebra three times and keep getting the wrong answer.

 

[gneill]

Sometimes when you hit a barrier due to a slip you can't see, it can help to change the approach slightly to take a different path to the solution. Why not try first reducing the voltage and R1, R2 to a Thevenin equivalent? You'll have two expressions for Vth and Rth (involving R1 and R2) but the result will be a purely series connected circuit.

 

[jdawg]

Thanks!