Potentiometer: Construction | Principal | Application | Sensitivity

An Ideal Voltmeter which does not change the original potential difference,needs to have infinite resistance. But a Voltmeter cannot be designed to have an infinite resistance. Potentiometer is one such device which does not draw any current from the circuiy and still measure the potential difference. So it acts as an ideal voltmeter.
Construction of Potentiometer

Potentiometer consist of a long wire,usually 10 m long, of material which have high resistivity and low temperature cofficient such us constantan. Usually, 1 m long separate pieces of the wires are are fixed on a wooden board which is parallel to each other. The wires are joined in series by thick copper strips. A meter scale is fixed parallel to the wires. The end A and B are coonected to a strong battery,a plug key K and a rheostat Rh. This circuit, called driving or auxiliary circuit , sends a constant current I through wire AB. Thus, the potential gradually falls from A to B. A jockey can slide along the length of the wire.
Principal of Potentiometer
The principle of the potentiometer is that when a constant current flows from a wire of uniform cross section area and composition, the potential drop across any length of the wire is directly proportional to that length.a
Potential Gradient - The potential drop per unit length of the potentiometer wires is is known as potential gradient.
    K = V/L
S.I unit -  v/m
Application of Potentiometer

 1. Comparison of emfs of two primary cell

Fig. shows the circuit diagram for the comparing the emfs of the two cells. A constant current is maintained in the potentiometer wire AB by means of a battery of emf E through a key K and rheostat Rh. Let E1 and E2 be the emfs of the two primary cells which are to be compared. The positive terminals of these cells are connected to the end  A of the potntiometer wire and their negative terminals are connected to a high resistance box R.B. ,  a galvanometer G and a jockey J through a two way key. A high R is inserted in the circuit from resistance  box R.B to prevent excessive current flowing through the galvanometer.
As a plug is inserted between a and c , the celk E1 gets introduced in the circuit. The jockey j is moved along the wire  AB till the galvanometer shows no deflection. Let the position of the jockey be j1 and length of the wire Aj1 =  l1. If k is the potential gradient along the wire AB , then the null point,
E1 = Kl1
By inserting the plug between b and c , the null point is again obtained for cell  E2. Let the balancing length be Aj2 = l2. Then
E2 = kl2
:: E2/E1 = l2/l1
If one of the two cells is a standard cell of known emf , then emf of the other cell can be determined. E2 = l2/l1 * E1
In order to get the null point on the potentiometer wire, it is necessary that the emf, E of the auxiliary battery must be greater than both E1 and E2.
 2. Internal resistance of a primary cell by a potentiometer

As shown in fig., the positive terminal of the cell pf emf E whose internal resistance r is to be measured is connected to the end A of the potentiometer wire and its negative terminal to a galvanometer G and jockey j. A resistance box R.B. is connected across the cell through a key k2.
Close the key k1. A constant current flows through the potentiometer wire. With key k2 kept open, move the jockey along AB till it balance the emf E of the cell. Let l1 be the balancing length of the wire. If k is the potential gradient, then emf of the cell be: E=kl1
With the help of resistance box R.B., introduce a resistance R and close key k2. Find the balance point for the terminal potential difference V of the call. If l2 is the balancing length, then 
V= kl2
E/V = l1/l2
Let r be the internal resistance of the cell. If current I flows through cell when it is shunted with resistance R, then from ohm's law we get
E = I(R + r) 
And V= IR
E/V = R + r /R = l1/l2
r/R = l1-l2/l2
:: internal resistance =  r =R [ l1-l2/l2]
Superiority of a potentiometer to a voltmeter.
Potentiometer is a null method device. Al null point , it does not draw any current from the cell and thus there is no potential drop due to the internal resistance of the cell. It measures the p.d. in an open circuit which is equal to the actual emf of the cell. On the other hand , potentiometer draws a small current from the cell for its operation. So it measures the terminal p.d. in a closed circuit which is less than the emf of the cell . That is why potentiometer is preferred over a voltmeter for measuring the emf of a cell.
 Potentiometer  Sensitivity
 1.  If is sensitive if it is capable of measuring very small potential differences 
 2. If it shows a significant change in balancing length for a small change difference being measured.
 Sensitivity of a potentiometer can be increased in two ways:
 1. For a given potential difference , the sensitivity can be increased by increasing the length of a potentiometer wire.
 2. For a potentiometer wire of fixed length, the potential gradient can be decreased by reducing the current in the circuit with the help of a rheostat.
Reference link:  Kirchhoff's Law | Problem Based on Kirchhoff's Law