Question about output voltages and impedances

[Mohamed Abdul]

Homework Statement

1. For the first measurement, a load resistance Rload = 119Ohms results in an output voltage V(OUT) = 11Volts. For the second measurement, Rload = 11Ohms results in an output voltage V(OUT) = 3.2Volts. From these two measurements, determine the output voltage V(OUT) when Rload = Rsource. You will have to first determine Rsourceand Vsource to answer this question. Express your answer in Volts. Note that the answers will not necessarily be consistent with any source we have seen but should not be unreasonable.

2. A voltage divider is used to determine the input impedance of an unknown circuit. The circuit of figure 1 in the Wikipedia entry on the voltage divider (https://en.wikipedia.org/wiki/Voltage_divider) is used as the model. Assume that Vin = 12Volts, Z1 = 410Ohms, and Vout = 58% of Vin. Determine the value of Z2 if you assume the input impedance is totally resistive.

Homework Equations

Vout = Vin(R2/(R1+R2))

The Attempt at a Solution

For the first problem, I knew that the greater Rload, the closer Vout would be to the actual source voltage. Thus I assumed that Vsource was 11Volts since 119 Ohms >> 11 Ohms. Plugging that in the equation where R1=R2, I got:

Vout = 11(R/2R) -> Vout = 11(1/2) -> Vout = 5.5 Volts.

For the second one, I used the voltage divider formula with the impedences and got:
.65Vin = Vin(Z2/(Z1+Z2)) -> .65Z1 + .65 Z2 = Z2 -> .65Z1 = .35Z2 -> .65(352)/.35 = Z2 = 653.714 Ohms.

Overall I feel like my work was correct but I'm unsure if I used the correct methods. These are a bit different than what we do in class so I'm not too sure.

 

[Mohamed Abdul]

This is what the circuit looks like for the first problem, by the way. As of now I have managed to figure out the second question but I am still struggling with this one.

 

[CWatters]

You have 2 unknowns (Vsource and Rsource) so you will need to write 2 equations using the two data points (119R, 11V and 11R, 3.2V) and solve them.

 

[Mohamed Abdul]

You have 2 unknowns (Vsource and Rsource) so you will need to write 2 equations using the two data points (119R, 11V and 11R, 3.2V) and solve them.

Is that the only way to figure out the solution. Isn't there another way to find the output voltage by looking at the relationships between the resistances and voltages?

 

[Mohamed Abdul]

You have 2 unknowns (Vsource and Rsource) so you will need to write 2 equations using the two data points (119R, 11V and 11R, 3.2V) and solve them.

I checked my answer using your method, and it was correct. Thank you very much for helping me.

 

[CWatters]

Yes your method might work because 119 Ohms >> 11 Ohms. That won't always be the case.