Potentiometer & Its Applications | Physics Class 12 - NEET PDF Download

What is Potentiometer?

Potentiometer working can be explained when the potentiometer is understood. It is defined as a three-terminal resistor having either sliding or rotating contact that forms an adjustable voltage divider. In order to use the potentiometer as a rheostat or variable resistor, it should have only two terminals with one end and the wiper.

Following are the terms used to describe types of potentiometers:

1. Slider pot or slide pot: This can be adjusted by sliding the wiper right or left with a finger or thumb.

2. Thumb wheel pot or thumb pot: This can be adjusted infrequently with the help of small thumb wheel which is a small rotating potentiometer.

3. Trimmer pot or trim pot: This can be adjusted once for fine-tuning of an electric signal.

Necessity of Potentiometer

• Practically voltmeter has a finite resistance (ideally it should be ∞). In other words, it draws certain current from the circuit. To overcome this problem a potentiometer  is employed because at the instant of measurment , it draws no current from the circuit.

Working Principle of Potentiometer 

• Any unknown potential difference is balanced on a known potential difference which is uniformly distributed over the entire length of a potentiometer wire.
  This process is termed as zero deflection or null deflection method.

Note :
(i) Potentiometer wire : Made up of alloys of manganin, constantan, eureka.
(ii) Special properties of these alloys are high specific resistance, negligible temperature co-efficient of resistance (α). This results in invariability of resistance of potentiometer wire over a long period.

Circuits of Potentiometer

• Primary circuit contains source of constant voltage & rheostat or Resistance Box.
• Secondary circuit contains battery & galvanometer.

➢ Potential gradient (x) (V/m)

• Potential difference corresponding to unit length of potentiometer wire is called potential gradient.
• Rate of growth/fall of potential per unit length of potentiometer wire is equal to potential gradient.
• Let r = 0 and R₁ = 0 then V_AB = E (max. in the ideal case) then x = E/L
  Unit and dimensions : (V/m ; MLT^-3A^-1)
• Always V_AB < E ; (∵ r + R₁ ≠ 0)
  x = V_AB/L
• Now V_AB = I R_P (R_P = resistance of potentiometer wire)
• Let ρ = Resistance per unit length of potentiometer wire
  
  current in primary circuit I
  
• If cross-sectional radius is uniform ⇒ x is uniform over the entire length of potentiometer wire.
• If I constant, then
  
•  'x' depends on → ρ, r , σ  etc.

➢ Factors affecting 'x' 

• If V_AB = constant and L = constant then for any change → x remains unchanged.
• If there is no information about V_AB then always take V_AB as constant so (x ∝ 1/L)
• If V_AB and L are constant :
• For any change like radius of wire, substance of wire (σ) there is no change in x.
• Any change in the secondary circuit results in no change in x because x is an element of primary circuit.

Note:

x_max or x_min on the basis of range of rheostat or resistance box (R.B.)

Applications of Potentiometer

Comparison of EMF's of two cells using potentiometer

• Consider the circuit arrangement of potentiometer given below used for comparison of emfs of two cells
  
• Positive terminals of two cells of emfs E₁ and E₂ (whose emf are to be compared) are connected to the terminals A and negative terminals are connected to jockey through a two way key K₂ and a galvanometer
• Now first key K₁ is closed to establish a potential difference between the terminals A and B then by closing key K₂ introduce cell of EMF E₁ in the circuit and null point junction J₁ is determined with the help of jockey.If the null point on wire is at length

  l₁ from A then
  E₁ = Kl₁
  Where K → Potential gradient along the length of wire

• Similarly cell having emf E₂ is introduced in the circuit and again null point J₂ is determined. If length of this null point from
  A is l₂ then
  E₂ = Kl₂
  Therefore
  E₁/E₂ = l₁/l₂
  This simple relation allows us to find the ratio of E₁/E₂

• if the EMF of one cell is known then the EMF of other cell can be known easily

Determination of internal resistance of the cell

• Potentiometer can also be used to determine the internal resistance of a cell
  
• For this a cell whose internal resistance is to be determined is connected to terminal A of the potentiometer across a resistance box through a key K₂
• First close the key K₁ and obtain the null point. Let l₁ be the length of this null point from terminal A then
  E = Kl₁
• When key K₂ is closed ,the cell sends current through resistance Box (R). If E₂ is the terminal
  Potential difference and null point is obtained at length l₂(AJ₂) then
  V = Kl₂
  Thus
  E/V=l₁/l₂
  But E = I(R+ r) and V = IR
  This gives
  E/V = (r+R)/R
  So (r + R)/R = l₁/l₂
  giving
  r = R(l₁/l₂-1)
• Using above equation we can find internal resistance of any given cell