Extremely Difficult Circuit Problem involving a potentiometer

[lilcho]

Homework Statement

The schematic below shows the simplest potentiometer that can be used to regulate the voltage supplied onto the electric load that has the resistance R. In such case, the variable resistance is made of the uniform piece of wire having total resistance R0 and length l and a sliding contact S that can be moved along the wire. Find the voltage V(x) across the resistance R as a function of the distance x of the sliding contact as shown below. Emf of the battery V0. Additionally, consider the case when R>>R0.

Homework Equations

Total Emf = Total Resistance * Total Current

The Attempt at a Solution

I don't know where to get started.

 

[gneill]

Suppose the potentiometer were replaced by two resistors, R1 and R2. Could you find the voltage across R in that case?

 

[haouRon]

Suppose the potentiometer were replaced by two resistors, R1 and R2. Could you find the voltage across R in that case?

what about the length l and the contact s?

 

[gneill]

what about the length l and the contact s?

Ignore them for the moment. They can be related to the resistor values later.

 

[haouRon]

I was able to figure out the voltage but i still wonder how i plug into be V in function of x. i need some help

 

[gneill]

If you've found the voltage in terms of the R1 and R2 that I suggested, then it is now just a matter of relating R1 and R2 to the geometry of the wire and slider. This can be done by looking at sums and ratios.

The problem states that the overall resistance of the potentiometer wire is R0 and has length l. Right away you should be able to see that resistors R1 and R2 should add up to R0, so that in series they have the same resistance as the potentiometer wire.

The position of the slider S can be between x = 0 and x = l. At any given position it 'cuts' the potentiometer into two sections corresponding to resistances R1 and R2. The two sections have lengths x and l - x, and these lengths should represent fractions of the total resistance R0 corresponding to their fractional lengths of the whole.

Given this information, can you write expressions for R1 and R2 as functions of x?

 

[haouRon]

Ok, i see. Thanks gneill, I'm going to try it out.

 

[lilcho]

I need some help. In this circuit does V0 = R + R1 +R2?

And can someone elaborate on putting the resistance as a function of x and L?

 

[gneill]

I need some help. In this circuit does V0 = R + R1 +R2?

No, voltage can't equal resistance; the units don't match. You need to look at the circuit as a voltage divider. The voltage of the supply is being 'divided' across R2 and the parallel combination of R and R1. You need to solve this problem first.

And can someone elaborate on putting the resistance as a function of x and L?

For a uniform bar of resistive material, the resistance of a linear piece of it is proportional to the length. So if the total length is, say, L, and the total resistance of the length is R, then a section of length x will have resistance (x/L)R.