Potentiometer

  Potentiometer

 Potentiometer: Potentiometer is a device which is used to measure potential difference between two points. It uses no current from the system to measure the potential difference . Hence it gives accurate values for the potential difference

Principle: It works on the principle of null deflection.

Construction: It consist of  a long wire AB of length L. and resistance R mounted on a wooden board. A emf source e is connected to this wire  as shown in below figure.

Diagram: 

 

The resistance per unit length is given by R / L.    

Let R / L = σ . 

R = L σ ------------(1)

The current passing through the wire AB is given by Ohms law as,

I = V_AB / R

I = V_AB  / L σ  ( from ( 1)

Let P be any point on the wire,  and AP be l. Thus resistance of  wire AP is 

R_AP =  l σ -------(2)

Now Potential drop   V_AP = I  R_AP  

From (2)

V_AP = I l σ  

V_AP = (V_AB  / Lσ)   l σ

 V_AP = (V_AB  / L)   l 

 V_AP  α   l   -----------------(V_AB  &  L) are constant)

 V_AB  / l =  constant --------(A)

                                          Equation A is called as potential gradient of wire.

If I is the current passing through wire by source E and r is the internal resistance of the cell, 

then Current is given By,

I = E / R+r

 Potentail  V_AB = IR 

 V_AB=(E / R+r)R 

If we consider Potential per unit length then,

 V_AB  / L =  (E / {R+r}L)R

 <<< Kelvin's Bridge│ │ Use of potentiometer>>> 

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