Determine the position of the slider on the pot

[Harrison01]

Homework Statement

A circuit shows a 10kΩ potentiometer with a 5kΩ load. Determine the position of the pot across point XX (taken across the 5kΩ load) when the voltage across the load is 3v

Homework Equations

The Attempt at a Solution

I DONT HAVE A CLUE...
Really stumped on this one an could do with some explaining this to me in as simpler terms as possible. sorry to sound thick...
I understand we split the 10kΩ resister into 2 so we have 2 5kΩ resisters in series and that we are looking for a ration but that is as far as i seem to understand.
Ive gone through previous posts but seem to get confused with x10k and (1-x)10k.
Please help as i have been on this for weeks and getting peed off with myself for not understanding it.

 

[gneill]

Homework Statement

A circuit shows a 10kΩ potentiometer with a 5kΩ load. Determine the position of the pot across point XX (taken across the 5kΩ load) when the voltage across the load is 3v

Homework Equations

The Attempt at a Solution

I DONT HAVE A CLUE...
Really stumped on this one an could do with some explaining this to me in as simpler terms as possible. sorry to sound thick...
I understand we split the 10kΩ resister into 2 so we have 2 5kΩ resisters in series and that we are looking for a ration but that is as far as i seem to understand.
Ive gone through previous posts but seem to get confused with x10k and (1-x)10k.
Please help as i have been on this for weeks and getting peed off with myself for not understanding it.

You haven't stated what voltage is supplying the potentiometer (and there's no circuit diagram attached).

The 10kΩ "pot" is divided into two pieces, but not always 5k + 5k; the potentiometer allows a continuous selection of splits, so long as the total of the two parts is always 10kΩ.

That's why you make one of them be x10kΩ and the other (1-x)10kΩ, letting x range from zero to 1. The two always sum to 10kΩ and x "selects" the sizes of the pieces.

 

[Harrison01]

Ok gneil sorry bout that, I have a supply voltage and at the current moment i can't upload the picture.

Where can i read up about the x10kΩ and (1-x)10kΩ because i haven't been able to find examples of it used anywhere.

 

[gneill]

Ok gneil sorry bout that, I have a supply voltage and at the current moment i can't upload the picture.

Where can i read up about the x10kΩ and (1-x)10kΩ because i haven't been able to find examples of it used anywhere.

The x and (1-x) are just a convenient mathematical way to specify that the potentiometer resistance is being divided into two parts. It's like taking a plank of length L and cutting into two pieces; If one of the pieces is of length x*L, then what's left must be of length (1-x)*L. The same thing is being done only with the resistance of the potentiometer.

Potentiometers are just voltage dividers, which you should have encountered plenty of examples of. The difference is that potentiometers allow one to manually select the ratio of the resistances comprising the divider. You might find some interesting background material if you do a web search on "potentiometer theory".

Here's a diagram to help you along:

 

[Harrison01]

Thanks Gneil.

I haven't really covered many pots, I'm doing my HNC via open learning and the one thing I'm finding is that sometimes its hard to visualise things without it physically in front of you.

So, because i have a pot with a wire connected to the wiper to some other point in the circuit, a resistor that goes to ground, what we really have is a Rheostat?

Could i not say take the 10k divide it by 9volt to give me 1111.1Ω per volt, times this by 6 to give me 6666.6 for the volt drop which would then give me the 3v i require. I would there fore have 3333.3Ωon the remained of the pot. This would give me a ratio of 3/6 which would equal 1/2 which could be expressed on a percentage scale of 0-100% as 50% or on a scale of 0-1 as 0.5.

 

[NascentOxygen]

So, because i have a pot with a wire connected to the wiper to some other point in the circuit, a resistor that goes to ground, what we really have is a Rheostat?

You can think of it as a rheostat but with 3 terminals.

Could i not say take the 10k divide it by 9volt to give me 1111.1Ω per volt,

You can do that sort of thing ONLY if all of the current through the top resistance of the pot also goes through the lower part of the pot. But in your case, it doesn't. Some of the current diverts through the load, R_L. You need to derive an equation for the output voltage in terms of R_a, R_b, and R_L. That sounds like 3 unknowns, but it's only 2 really, because you know a relationship between R_a and R_b.

 

[Harrison01]

how bad is this, xmas eve and I am frying mt brain tyring to get my head around this question.

Ok, i under stand the equation and the working practice behind it all but the part I am struggling with is the ratio part. how do i go about working out the correct ratio of r1 and r2?
Whatever figure i get for r2 i have to involve the r3 (5kΩ) load (resistors in parrallel) and combine them to make 1.

Any help making me understand the ratio would be much appreciated.

 

[gneill]

how bad is this, xmas eve and I am frying mt brain tyring to get my head around this question.

Ok, i under stand the equation and the working practice behind it all but the part I am struggling with is the ratio part. how do i go about working out the correct ratio of r1 and r2?
Whatever figure i get for r2 i have to involve the r3 (5kΩ) load (resistors in parrallel) and combine them to make 1.

Any help making me understand the ratio would be much appreciated.

Take a look at the right-hand circuit in the image I posted. Can you write an expression for V_out in terms of E, R_a, R_b, and R_L?

 

[Harrison01]

My expression for vout would surely be using the correct formula to give me the combined resistance of Ra & Rl but since i don't know the value of Ra how do i go about working it out?
My equation for the Vout would be E*Ra/Rb+Ra=Vout but since we already know this is 3v there must be a way of transposing this? Are my terms of thinking correct or is it back to the drawing board..

 

[gneill]

My expression for vout would surely be using the correct formula to give me the combined resistance of Ra & Rl but since i don't know the value of Ra how do i go about working it out?
My equation for the Vout would be E*Ra/Rb+Ra=Vout but since we already know this is 3v there must be a way of transposing this? Are my terms of thinking correct or is it back to the drawing board..

You're on the right track. You begin by writing equations describing and relating the things you know with the things that you don't.

I think you already see that E*Ra/Rb+Ra=Vout isn't going to work, since Ra has RL in parallel with it and will so RL will conduct some current too, perturbing the output by some amount (more current will flow through Rb, so more voltage will be dropped across it).

The general voltage divider consists of two resistors. Here the "bottom" resistor is made up of the parallel pair of Ra and RL. What's an expression for the net resistance that this pair represents (maybe call it "Rp" for "R parallel)?

Now write the voltage divider formula using this expression for the bottom resistor value. The top resistor remains the same, Rb.

 

[Harrison01]

Ok since we have realistically made our Parrallel resisters as one (Rp) our circuit has now become an open circuit or output voltage under no load condition with just 2 resitors in series, Vout=E*Rp/(Rb+Rp) but isn't this the same equation as my last post?

 

[gneill]

Ok since we have realistically made our Parrallel resisters as one (Rp) our circuit has now become an open circuit or output voltage under no load condition with just 2 resitors in series, Vout=E*Rp/(Rb+Rp) but isn't this the same equation as my last post?

It's not the same... it has a different resistance, Rp, for which you can write an expression and substitute for it. What's the expression for Rp?

 

[Harrison01]

Well the expression for Rp is Ra+Rl which would give me an equation of Vout=E*Ra+Rl/(Rb+Ra+Rl) I think...

 

[gneill]

Well the expression for Rp is Ra+Rl <snip>

Nope. That's not the expression for two resistors in parallel. That's for two resistors in series... What's the expression for two resistors in parallel?

 

[Harrison01]

2 resistors in parallel is Rp=Ra*Rl/Ra+Rl.

 

[gneill]

2 resistors in parallel is Rp=Ra*Rl/Ra+Rl.

Okay, make that substitution for Rp into the voltage divider expression.

When that's done, think about what you know about Ra and Rb and the resistance value of the potentiometer, Rpot.

 

[Harrison01]

Think I'm starting to wander off the track a bit here but still, here goes. Vout=E*Ra*Rl/Ra+Rl/Rb+Ra/Ra*Rl/Ra+Rl

I know that Ra and Rb must equal a total of 10k ohms and the higher the Rb figure the higher the reistance and vice versa for Ra.

 

[gneill]

can you put some parentheses into that expression so we can tell the order of operations?

 

[Harrison01]

Gneil, cheers for bearing with me. are you at your wits end yet?
Ok, think I'm right here Vout=E*(Ra*(Rl/Ra+Rl))/(Rb+Ra/Ra)*(Rl/Ra+Rl)
The only thing I'm still struggling to see here is how this will give me the values of Ra and Rb

 

[gneill]

Gneil, cheers for bearing with me. are you at your wits end yet?

I'm told that I've been witless for years now

Ok, think I'm right here Vout=E*(Ra*(Rl/Ra+Rl))/(Rb+Ra/Ra)*(Rl/Ra+Rl)
The only thing I'm still struggling to see here is how this will give me the values of Ra and Rb

Okay, as I suspected something's gone amiss with your voltage divider expansion/simplification. Note that terms like (Rb + Ra/Rb) can't exist due to unit issues; Rb has units of Ohms and Ra/Rb has no units. You can't add a unitless number to one with units. You'll have to try the simplification again I'm afraid. There should be pairwise products of resistors in the expression. If you are having trouble, you can always post your simplification steps for review.

Once you have that straightened out, you'll write what you know about Ra, Rb, and their total as an equation. Then you'll have two equations in two unknowns.

Alternatively, make the immediate substitutions Ra = x*R; Rb = (1-x)*R, where R is the resistance of the potentiometer. Solve for x, the portion of the potentiometer that represents resistor Ra.

 

[Harrison01]

Ok, round 2

Vout= E* Ra*Rl/(Rb*Rl)+(Ra*Rl)+(Rb*Ra)

 

[gneill]

Ok, round 2

Vout= E* Ra*Rl/(Rb*Rl)+(Ra*Rl)+(Rb*Ra)

Presumably that's:

Vout= E* Ra*Rl/[(Rb*Rl)+(Ra*Rl)+(Rb*Ra)]

Square parentheses added to really nail down the order of operations, and that would be correct

Now proceed as indicated (my previous post) to solve for Ra (or directly for x).

 

[Harrison01]

Yeah that's what i meant Gneil.

Getting somewhere at least.

Now i must be incredibly here thick but how can i carry out the maths if i don't have figures to put in the places of Ra & Rb. I just don't see how putting X or (1-X) helps. I understand that they are relevant to a ratio but if i don't have number to put in how can i work it out.

 

[Harrison01]

So by using the equation i have

9*Ra*5000/[(Rb*Ra)+(Rb*5000)+(Rb*Ra)]

9*x*R*5000/[((1-x)*R*x*R)+((1-x)*R*5000)+((1-x)*R*x*R)]

 

[gneill]

So by using the equation i have

9*Ra*5000/[(Rb*Ra)+(Rb*5000)+(Rb*Ra)]

9*x*R*5000/[((1-x)*R*x*R)+((1-x)*R*5000)+((1-x)*R*x*R)]

Okay, now that whole thing is going to equal 3, or Vout, right? And what is the value of R?

 

[Harrison01]

Yeah Vout equals 3v and R is 10kohms

 

[gneill]

So, solve for x.

 

[Harrison01]

So I'm thinking x=Vout/10kohms=3/10000=0.0003ma

 

[gneill]

So I'm thinking x=Vout/10kohms=3/10000=0.0003ma

What happened to the equation you spent so much time deriving? x should be a unitless number, representing the fraction of the potentiometer that is Ra.

 

[Harrison01]

What happened to the equation you spent so much time deriving? x should be a unitless number, representing the fraction of the potentiometer that is Ra.

I just can't get in my thick skull...

 

[gneill]

I just can't get in my thick skull...

Refer to the diagram in post #4.

 

[Harrison01]

What happened to the equation you spent so much time deriving? x should be a unitless number, representing the fraction of the potentiometer that is Ra.

Ok i understand that x and (x-1) are unitles numbers as we yet don't know their value but we do know that their value sums up to 10kohms. We therefore need to work out the ratio. We know we have a Vout of 3v and that Rl is 5kohms. I just can't seem to understand how we use all this data to give us the value of Ra or Rb which will then give us the opposing figure.

 

[gneill]

Ra is x*R. Rb is (1-x)R. R is the value of the potentiometer, 10000 Ohms.

Ra + Rb = R

x*R + (1-x)*R = R

x is just a value that "cuts" the potentiometer into two pieces. The two pieces sum to the whole.

 

[braceman]

I haven't touched anything like this in years and was following this through ok till i hit post 21 and 22.

Could someone please explain how we specifically get the (Rb*Rl)+(Ra*Rl)+(Rb*Ra) part of Vout= E* Ra*Rl/[(Rb*Rl)+(Ra*Rl)+(Rb*Ra)]

I just can't see why its Rb X Rl + the rest..

Could someone show or explain how these 3 are derived.
I would be very grateful.

 

[gneill]

I haven't touched anything like this in years and was following this through ok till i hit post 21 and 22.

Could someone please explain how we specifically get the (Rb*Rl)+(Ra*Rl)+(Rb*Ra) part of Vout= E* Ra*Rl/[(Rb*Rl)+(Ra*Rl)+(Rb*Ra)]

I just can't see why its Rb X Rl + the rest..

Could someone show or explain how these 3 are derived.
I would be very grateful.

Expand the expression for the output of the voltage divider using the given components.