Potentiometer
A potentiometer is an instrument used to measure emf of a cell or potential difference across a resistor in a circuit. Its construction consists of a long stretched wire and mounted on a wooden board with two terminals A and B. The resistance varies with the length of terminal AB.
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The Principle of potentiometer:
The potential difference across any section of a wire of length l, carrying a steady current is directly proportional to the length of the wire. The cross-section area of the wire should be uniform throughout and the wire should be of the same material.
Mathematically,
Potential difference (V) ∝ Length of the section of the wire (l)
Proof:
We know from Ohm’s law, the potential difference across the section of wire is V = IR if R is the resistance of that section of the wire.
V = I * ρl/A
where 'I' is steady current; 'ρ' is the density of wire and 'A' is the area of cross-section.
For constant I, A and ρ we can write,
V ∝ l
i.e. the potential difference across a section of the wire is directly proportional to the length of that section.
Potentiometer Basics
Potentiometer consists of a long wire AB of length L placed on a wooden board. The potentiometer wire has a uniform area of cross section and has constant resistivity throughout. A DC source E’ is connected to the potentiometer terminals AB through an ammeter and a rheostat. This emf source E’ is called driving emf and is very important to maintain steady current in the potentiometer wire during measurement. The rheostat is used to vary currents in the potentiometer wire varying resistance and the ammeter is used to measure the current in the wire.
Let us take any point 'X' in the potentiometer wire where 'I' current is maintained by driving emf E’ as shown in the figure. The resistance of potentiometer wire AB with the area of cross section A, resistivity ρ and length L is,
Rab = ρL/A
Then current, I = E’/Rab = E’/(ρL/A)
If l is the length of segment AX, then resistance of segment AX is,
Rax = ρl/A
Voltage drop in the segment of the wire is,
Vac = IRax = E’/(ρL/A)ρl/A = (E’/L)l
Thus, Vac = (E’/L)*l . For a potentiometer E’ and L are constant. So, Vac∝ l.
This E’/L value is constant for the particular arrangement of potentiometer known as potentiometer constant (k).
In potentiometers available in labs, the length of the wire may vary. Longer the potentiometer wire, greater is the sensitivity of the potentiometer. This is because greater length L means less value of E’/L. Due to this potential dropped per unit length of the section of the wire will be less. In other words, in large wire section potential difference is less so clearly sensitivity increases.
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