Thevenin Voltage Value Homework

[mrowa196]

Homework Statement

I calculated theoretical value of resistance - I assumed that R4 and R5 are in series and parallel to R2 and R3 which are in series, because I've considered B as the starting point - this is the method I was taught, but I don't know any method of calculating the voltage with the diode. Experimental value of voltage was about 3.75 V.

 

[gneill]

There's not enough data to arrive at a numerical result. Were you not given component values?

 

[NascentOxygen]

I calculated theoretical value of resistance - I assumed that R4 and R5 are in series and parallel to R2 and R3 which are in series, because I've considered B as the starting point - this is the method I was taught, but I don't know any method of calculating the voltage with the diode. Experimental value of voltage was about 3.75 V.

What are the resistance ratios you were given?

 

[mrowa196]

Oh, I am sorry, I thought it was on the diagram:

R2 = 5.6 kΩ, R3 = 2.7 kΩ, R4 = 6.8 kΩ, R5 = 3.3 kΩ

R1 is apparently not necessary.

 

[NascentOxygen]

Suppose R3 and R4 (and, for good measure, point B) were all erased from the drawing, could you calculate the voltage V_A with respect to the lower end of the zener?

 

[cnh1995]

If I understand the problem correctly, it is asked to find V_AB i.e. the Thevenin voltage. Assuming the zener diode is in reverse breakdown region, voltage across it will be 6.2V, fixed. I believe the OP has assumed correct series-parallel combinations. But the voltage value I am getting is not 3.75V, which is obtained experimentally as said. Is there something wrong with the experimental value?

 

[mrowa196]

I've also measured the current and calculated experimental resistance and it was 4.64 Ohms, so very close to theoretical value of 4.60 Ohm. Hence, I think it was pretty accurate experiment.

 

[cnh1995]

I've also measured the current and calculated experimental resistance and it was 4.64 Ohms, so very close to theoretical value of 4.60 Ohm. Hence, I think it was pretty accurate experiment.

Was the zener diode in breakdown region? I mean was the voltage across it 6.2V? If yes, I think V_AB should be 2.14V.

 

[mrowa196]

The voltage applied was 12V.

Edit: I'm sorry. I measured the current and voltage for three applied voltages: 12, 15 and 18 V, but I need the value for 12V. I need to measure maximum theoretical power transfer.

 

[cnh1995]

The voltage applied was 12V.

Edit: I'm sorry. I measured the current and voltage for three applied voltages: 12, 15 and 18 V, but I need the value for 12V. I need to measure maximum theoretical power transfer.

Still if the zener voltage is maintained at 6.2V, V_AB will be same regardless of the supply voltage. Only the value of R1 will change.

 

[mrowa196]

Or maybe there is no enough information and I need to use the experimental value of voltage. After all what I need is to compare maximum theoretical power transfer and maximum experimental power transfer. Maybe I can only compare it by using theoretical value of resistance for one and experimental value of resistance for another while the voltage value would be experimental in both cases.

Edit: I read the problem again and it says specifically I need to use BOTH THEORETICAL values...

 

[mrowa196]

What if I ignored R3 and R4 part of the circuit and I would be left with:

Then I ignore R1 and 15 V source part and I would be just left with 6.2 "source" let's say and two resistors circuit. Then, using voltage dividor rule and the values of resistances of the resistors (5.6/(5.6+3.3))*6.2. That would give 3.9V at point A which is close enough to experimental value, but I just made this method up so I think it's bullshit.

 

[gneill]

Edit: I read the problem again and it says specifically I need to use BOTH THEORETICAL values...

Can you share the actual problem statement with us?

 

[mrowa196]

It's actually a lab report, so it's a whole document, but it's only one part of it - maximum power transfer.

 

[gneill]

The lab asks that you identify the values for resistors R2 and R4. What was involved in doing that?

 

[mrowa196]

Reading from the colour codes. That was checked - they are correct.

 

[gneill]

Did you also confirm that the other resistors (R3 and R5) actually had the values shown in the lab diagram?

I'm trying to understand how you could have measured 3.75 V across AB given this circuit arrangement. If the zener really is a 6.2 V one, then I'm not seeing a way to achieve this with the given component values.

 

[mrowa196]

Yes, I have. The resistances must be correct because theoretical and experimental values of resistances are almost identical.

 

[mrowa196]

I found the photo of the circuit.

 

[gneill]

Looking at the photo, I question whether the color code for R4 is Blue-Violet-Red (6.8 k) or Blue-Violet-Orange (68 k). If it's the latter it might explain your measured voltage. It would push it to around 3.8 V.

What short circuit current did you measure?

 

[mrowa196]

0.8 mA

 

[gneill]

0.8 mA

With what supply voltage?

 

[mrowa196]

12 V

 

[gneill]

Okay, with R4 at 68 kΩ I can see you measuring about 3.75 V and 0.8 mA. With those values your Thevenin resistance should be in the kilo-Ohms, not just a few Ohms. So something around 4.7 kΩ.

 

[mrowa196]

Yes, you're right, I've actually went through my notes and there is 68000 kΩ written but I've crossed one 0, because I could not get theoretical value of Thevenin resistance close the he experimental one otherwise... Did you get it?

Experimental data:

 

[gneill]

Yes, I can calculate about 4.7 kΩ for the Thevenin resistance, which corresponds nicely with your table values.

 

[mrowa196]

Could you please walk me through your calculations?

 

[NascentOxygen]

What if I ignored R3 and R4 part of the circuit and I would be left with:
View attachment 93993
Then I ignore R1 and 15 V source part and I would be just left with 6.2 "source" let's say and two resistors circuit. Then, using voltage dividor rule and the values of resistances of the resistors (5.6/(5.6+3.3))*6.2. That would give 3.9V at point A which is ...

That's half the working. Then follow a similar procedure to determine V_B. Using these results, you can calculate the value for V_AB.

 

[NascentOxygen]

Could you please walk me through your calculations?

The zener is a good voltage source, so replace it with a short circuit.

 

[mrowa196]

How about the resistance? I've had this:

But despite good result it must be wrong, because it shouldn't be 6.8 but 68 kOhms.

 

[gneill]

Here's another rendering of your circuit with the components rearranged into a more common pattern:

If the zener is replaced by a short (not a bad approximation since it should have a zener resistance of just a few Ohms when in "zener mode") can you reevaluate your method for determining the Thevenin resistance?

 

[mrowa196]

Great, that diagram of yours explains everything about the voltage.

The method for determining the Thevening resistance from my lecture notes is here:

In the original circuit there is voltage source on the left, so you ignore it, look at the circuit from the right and then 6 Ohm is in series with 2 Ohm and 3 Ohm in parallel.

 

[gneill]

Yes, that's a good example. Now, what do you make of the circuit in question? When the zener is replaced by a short, what opportunities for combining resistors do you find?

 

[mrowa196]

I still see it as in the beginning: R4 and R5 are in series and parallel to R2 and R3 which are in series :/

 

[gneill]

I still see it as in the beginning: R4 and R5 are in series and parallel to R2 and R3 which are in series :/

Nope. R3 and R4 can't be in series because the zener also connects to their junction. Same goes for R4 and R5.

Look for resistor pairs whose terminals share the same connections (pay attention to the "short" that the zener now represents!).

When in doubt take some highlighter pens and color code the separate nodes. Look for resistors with the same two node connections (color pairs).

 

[cnh1995]

How did you get 470Ω here?

According to the simulation I ran, I got 400Ω there.

 

[gneill]

How did you get 470Ω here?

I read the color code on the resistor in the provided image

 

[cnh1995]

I read the color code on the resistor in the provided image

Oh..!Beause I could not theoretically determine R1. But once the zener is shorted, R1 won't be a part of the circuit, right?

 

[gneill]

Oh..!Beause I could not theoretically determine R1. But once the zener is shorted, R1 won't be a part of the circuit, right?

Right. That's a valid approximation since the zener resistance is small compared to the other resistances in the circuit. So R1 will effectively be shorted, too.

In a more stringent analysis, one might find the resistance of the zener under operating conditions to be, say ten Ohms or so. Maybe less. Maybe a tad more. If it came down to such details then you'd look for a datasheet for the particular zener and pull up a value from there.

 

[cnh1995]

Right. That's a valid approximation since the zener resistance is small compared to the other resistances in the circuit. So R1 will effectively be shorted, too.

In a more stringent analysis, one might find the resistance of the zener under operating conditions to be, say ten Ohms or so. Maybe less. Maybe a tad more. If it came down to such details then you'd look for a datasheet for the particular zener and pull up a value from there.

Right!

 

[mrowa196]

How about R3 being in parralel with R4, but in series with R2 and R5 in parralel? That gives me something about 4.5 after quick calculation.

 

[cnh1995]

How about R3 being in parralel with R4, but in series with R2 and R5 in parralel? That gives me something about 4.5 after quick calculation.

You mean (R3 ll R4) in series with (R2 ll R5)? Looks correct to me!

 

[mrowa196]

Thank you all very much! I understand it completely now ;)

 

[NascentOxygen]

You calculated the theoretical value for V_AB somewhere?

 

[mrowa196]

I used this diagram and potential divider calculations to get the voltage at A and B and that gave me a good result

Here's another rendering of your circuit with the components rearranged into a more common pattern:
View attachment 94003

If the zener is replaced by a short (not a bad approximation since it should have a zener resistance of just a few Ohms when in "zener mode") can you reevaluate your method for determining the Thevenin resistance?

At point A: 5.6/(5.6+3.3)*6.2 = 3.90
At point B: 2.7/(68+2.7)*6.2 = 0.24

The difference would be 3.66. Correct?

 

[gneill]

Looks good.

If you want to obtain a more accurate theoretical value for V_AB, replace the zener with a suitable equivalent model and analyze the full circuit. For example, a 6.2 V source in series with a 10 Ω resistor would probably be a pretty good starting point for a model for the zener.

You could then combine the 12 V source and its 470 Ω resistor with the zener model to form a Thevenin equivalent source that drives the bridge. Then tackle the resulting circuit.

 

[nathsen]

Here's another rendering of your circuit with the components rearranged into a more common pattern:
View attachment 94003

If the zener is replaced by a short (not a bad approximation since it should have a zener resistance of just a few Ohms when in "zener mode") can you reevaluate your method for determining the Thevenin resistance?

Hi, I understand how R2 ll R5 and R3 ll R4 but what is the reasoning for R2 and R3 being in series and same for R4 and R5? Thanks

 

[gneill]

Hi, I understand how R2 ll R5 and R3 ll R4 but what is the reasoning for R2 and R3 being in series and same for R4 and R5? Thanks

Redraw the circuit in post #46, suppressing the voltage source (ignoring its small resistance) and placing identified parallel resistances next to each other:

Does that help?

 

[nathsen]

Redraw the circuit in post #46, suppressing the voltage source (ignoring its small resistance) and placing identified parallel resistances next to each other:

View attachment 99869

Does that help?

Redraw the circuit in post #46, suppressing the voltage source (ignoring its small resistance) and placing identified parallel resistances next to each other:

View attachment 99869

Does that help?

Thanks again for your reply. So, to identify two components are in parallel I can identify that two components share the same pair of nodes. What's the definitive method to determine a component is in series with another? How do I come to the conclusion that they are in series from your diagram? Or are they only considered to be in series once both pair of parallel resistors are added?

 

[gneill]

Thanks again for your reply. So, to identify two components are in parallel I can identify that two components share the same pair of nodes. What's the definitive method to determine a component is in series with another? How do I come to the conclusion that they are in series from your diagram? Or are they only considered to be in series once both pair of parallel resistors are added?

It's the pairs of parallel resistors that are in series, not the resistors individually. The parallel pairs can both be simplified to single resistance values, and those resistors will be in series (share one node exclusively).