What is the concept behind varying resistance in a voltage divider circuit?

[logearav]

Homework Statement

Dear Members,
I have attached two diagrams found in Voltage divider topic found in web , while discussing about potentiometer . My doubt is, in the first attachment( Voltage Divider.png) when the wiper( the one with arrow mark) is moved towards the top, that is towards the terminal 1, it has been mentioned terminal 1 will have less resistance and terminal 2 will have more resistance.
Similarly, if the wiper is moved towards terminal 2, terminal 2 will have less resistance than terminal 1. What is the concept involved here?

Going by the same argument, in my second attachment(Voltage Divider1.png), the wiper is moved down, the dark black point in the diagram should have less resistance and more current, so more voltage drop. Am i interpreted the second diagram correctly?

Homework Equations

The Attempt at a Solution

 

[kuruman]

My doubt is, in the first attachment( Voltage Divider.png) when the wiper( the one with arrow mark) is moved towards the top, that is towards the terminal 1, it has been mentioned terminal 1 will have less resistance and terminal 2 will have more resistance.
Similarly, if the wiper is moved towards terminal 2, terminal 2 will have less resistance than terminal 1. What is the concept involved here?

The terminals do not have resistance. The concept involved here is that if the wiper is moved up the resistance between "1" and the wiper decreases, while the resistance between the wiper and "2" decreases. When the wiper is all the way up, the resistance between "1" and the wiper is zero while the resistance between the wiper and "2" has its maximum value.

Going by the same argument, in my second attachment(Voltage Divider1.png), the wiper is moved down, the dark black point in the diagram should have less resistance and more current, so more voltage drop. Am i interpreted the second diagram correctly?

Again, points don't have resistance. The resistance is between the wiper and the dark black point at the bottom. As the wiper is moved down, the resistance between the wiper and the dark point at the bottom decreases as I just said. Now the current provided by the battery stays same because the resistance between the top dark point and the bottom dark point does not change if you move the wiper. Since V = IR, when R decreases while I stays the same, V has to decrease.

 

[logearav]

The terminals do not have resistance. The concept involved here is that if the wiper is moved up the resistance between "1" and the wiper decreases, while the resistance between the wiper and "2" decreases. When the wiper is all the way up, the resistance between "1" and the wiper is zero while the resistance between the wiper and "2" has its maximum value.

Sir, but why the resistance between "1" and the wiper decreases, if the wiper is moved up?

 

[gneill]

Sir, but why the resistance between "1" and the wiper decreases, if the wiper is moved up?

The potentiometer consists of a strip of resistive material (with a resistance of so many Ohms per meter), with a sliding wiper contact that can move along that strip. Contacts are attached to the two ends of the strip and the wiper forms a third contact. When the position of the wiper changes, the distances between the point of contact of the wiper and the ends of the strip changes. The resistance between two points of contact on the strip depends upon the distance between them. Smaller distance --> less resistance. Larger distance --> larger resistance.

 

[logearav]

Thanks Mr. Kurumman and Mr. Gneill for your replies.
Mr. Gneill, do the equation R $\alpha$ l/A, hold good in this situation?

 

[gneill]

Mr. Gneill, do the equation R $\alpha$ l/A, hold good in this situation?

If l is the length and A the cross sectional area, then yes, it holds in general. But in this particular case the resistivity constant is defined so that the cross sectional area is taken into account and only the length is a variable. $R \propto L$.