Friday, May 29, 2015

Potentiometer

Potentiometer is a device mainly used to measure emf of a given cell and to compare emf's of cells. It is also used to measure internal resistance of a given cell.
Circuit diagram: Potentiometer consists of a long resistive wire AB of length L (about 6 m to 10 m long) made up of manganin and constantan and a battery of known voltage e and internal resistance r called supplier battery or driver cell. Connection of these two forms primary circuit.
One terminal of another cell (whose emf E is to be measured) is connected at one end of the main circuit and the other terminal at any point on the resistive wire through a galvanometer G. This forms the secondary circuit. Other details are as followsCircuit diagramJ = Jockey
K = Key
R = Resistance of potentiometer wire,
r = Specific resistance of potentiometer wire.
Rh = Variable resistance which controls the current through the wire AB

Points to be taken care of

  • The specific resistance (r) of potentiometer wire must be high but its temperature coefficient of resistance (a) must be low.
  • All higher potential points (terminals) of primary and secondary circuits must be connected together at point A and all lower potential points must be connected to point B or jockey.
  • The value of known potential difference must be greater than the value of unknown potential difference to be measured.
  • The potential gradient must remain constant. For this the current in the primary circuit must remain constant and the jockey must not be slided in contact with the wire.
  • The diameter of potentiometer wire must be uniform everywhere.


Potential gradient (k): Potential difference (or fall in potential) per unit length of wire is called potential gradient i.e. k = V/L volt/m where V = iR = (e/R+Rn+r)R.
So k = V/L = iR/L = ip/A = e/(R+Rh+r) . R/L
(i) Potential gradient directly depends upon
   (a) The resistance per unit length (R/L) of potentiometer wire.
   (b) The radius of potentiometer wire (i.e. Area of cross-section)
   (c) The specific resistance of the material of potentiometer wire (i.e. r)
   (d) The current flowing through potentiometer wire (i)
(ii) Potential gradient indirectly depends upon
   (a) The emf of battery in the primary circuit (i.e. e).
   (b) The resistance of rheostat in the primary circuit (i.e. Rh).

Working: Suppose jockey is made to touch a point J on wire then potential difference between A and J will be V = kl
At this length (l) two potential difference are obtained
(i) V due to battery e and
(ii) E due to unknown cellIf V > E then current will flow in galvanometer circuit in one direction 
If V < E then current will flow in galvanometer circuit in opposite direction 
If V = E then no current will flow in galvanometer circuit this condition to known as null deflection position, length l is known as balancing length.
In balanced condition E = xl
or E = xl = V/L l = iR/L l = (e/R+Rh+r) × R/L × l
If V is constant then L ∝ l ⇒ x1/x2 = L1L2 = l1/l2

Standardization of Potentiometer: The process of determining potential gradient experimentally is known as standardization of potentiometer.Let the balancing length for the standard emf E0 is l0 then by the principle of potentiometer E0 = xl0 ⇒ x = E0/l0

Sensitivity of potentiometer: A potentiometer is said to be more sensitive, if it measures a small potential difference more accurately.
(i) The sensitivity of potentiometer is assessed by its potential gradient. The sensitivity is inversely proportional to the potential gradient.
(ii) In order to increase the sensitivity of potentiometer
(a) The resistance in primary circuit will have to be decreased.
(b) The length of potentiometer wire will have to be increased so that the length may be measured more accuracy.
Difference between voltmeter and potentiometer
Voltmeter
Potentiometer
It's resistance is high but finite
It's resistance is infinite
It draws some current from source of emf
It does not draw any current from the source of unknown emf
The potential difference measured by it is lesser than the actual potential difference
The potential difference measured by it is equal to actual potential difference
Its sensitivity is low
Its sensitivity is high
It is a versatile instrument
It measures only emf or potential difference
It is based on deflection method
It is based on zero deflection method
 Click here for Application's of Potentiometer
 Click here for Numerical's on Potentiometer

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