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**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 R
_{1 }= 0 then V_{AB}= E (max. in the ideal case) then x = E/L

Unit and dimensions : (V/m ; MLT^{-3}A^{-1}) - Always V
_{AB}< E ; (∵ r + R_{1}≠ 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 E
_{1}and E_{2}(whose emf are to be compared) are connected to the terminals A and negative terminals are connected to jockey through a two way key K_{2}and a galvanometer - Now first key K
_{1}is closed to establish a potential difference between the terminals A and B then by closing key K_{2}introduce cell of EMF E_{1}in the circuit and null point junction J_{1}is determined with the help of jockey.If the null point on wire is at lengthl

_{1}from A then

E_{1}= Kl_{1}

Where K → Potential gradient along the length of wire Similarly cell having emf E

_{2}is introduced in the circuit and again null point J_{2}is determined. If length of this null point from

A is l_{2}then

E_{2}= Kl_{2}

Therefore

E_{1}/E_{2}= l_{1}/l_{2}

This simple relation allows us to find the ratio of E_{1}/E_{2}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 K
_{2} - First close the key K
_{1}and obtain the null point. Let l_{1}be the length of this null point from terminal A then

E = Kl_{1} - When key K
_{2}is closed ,the cell sends current through resistance Box (R). If E_{2}is the terminal

Potential difference and null point is obtained at length l_{2}(AJ_{2}) then

V = Kl_{2}

Thus

E/V=l_{1}/l_{2}

But E = I(R+ r) and V = IR

This gives

E/V = (r+R)/R

So (r + R)/R = l_{1}/l_{2}

giving

r = R(l_{1}/l_{2}-1) - Using above equation we can find internal resistance of any given cell

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