Potentiometer

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Principle of Potentiometer:

  • When a steady current flows through a wire of uniform cross-section the potential difference per unit length of the wire is constant throughout the length of the wire (or p.d. across any two points of the wire is directly proportional to the length of the wire.
  • It can be explained as below.



  • Let us consider a uniform wire AB of length lAB and uniform cross-sectional area  A. Let RAB be its resistance. Let ‘I’ be the steady current flowing through the wire. Let  VAB be the p.d. across the ends of the wire. Let ‘ρ be the specific resistance of the material of wire. Let there be uniform potential drop across the length of wire.

Potentiometer 01

Let us consider point P on the wire and the length of wire between A and P be ‘ lAP

Thus, the resistance of wire of length ‘RAP’ is given by

Potentiometer 02

  • When a constant current flows through a wire, then the potential difference between any two points of the wire is directly proportional to the length of wire between these two points. In such case, the  p.d. per unit length of the wire is constant and called potential gradient of the wire or voltage drop across the wire.

Advantages of a Potentiometer Over a Voltmeter:

  • A potentiometer can be used to measure the internal resistance of cell which can not be measured by the voltmeter.
  • A Potentiometer can be to measure e.m.f of a cell which can not be measured by a voltmeter. When a voltmeter is connected in a circuit it draws current through the circuit and thus can measure the potential difference across the cell terminals. When the potentiometer is connected in a circuit it draws no current when the null point is obtained. Thus it measures the e.m.f. of the cell.
  • A potentiometer can be used to measure extremely small p.d. accurately which cannot be measured by a voltmeter. It can be done by using very long wire and adjusting very small potential gradient.
  • Potentiometer is more sensitive compared to voltmeter.
  • The accuracy of potentiometer can be increased by increasing the length of wire. The accuracy of voltmeter cannot  be increased beyond the limit.



Construction of Potentiometer:

Potentiometer 09

  • A potentiometer consists of a uniform wire AB several meters long.  It is stretched between two points A and B on the wooden board.
  • A battery having a sufficiently large e.m.f. E is connected between A and B of the wire.  On closing, the key current will flow through the wire.
  • The current in the wire can be adjusted by adjusting rheostat connected in series with the battery.  The battery maintains a uniform potential gradient along the length of wire.

Working or Use of Potentiometer:

Measure e.m.f. of a Cell or to Compare e.m.f.s of Two Cells by Individual Method

Potentiometer 04

  • Let E1 and E2 be the e.m.f.’s of the two cells to be compared by using the potentiometer. The positive terminal of the cell of e.m.f. E1 is connected to end A and negative terminal is connected to jockey through galvanometer. By closing the key the jockey is moved along wire AB and null point P is determined such that galvanometer shows no deflection. The length of wire AP =l1, is measured.  The p.d. across this length balances e.m.f. E1

e.m.f. of the cell =  potential difference across AP

E1 = K l1 ………..  (1)

where K is the Potential gradient of the wire

  • Then cell of e.m.f. E1, is disconnected and cell of e.m.f. E2, is connected in circuit and procedure is repeated

E2 = K l2 ………..   (2)

Dividing equation  (1) by (2), we get,

Potentiometer 05

Thus knowing the values of l1 and lwe can compare e.m.f.s of two cells.



Measure e.m.f. of a Cell or to Compare e.m.f.s of Two Cells by Sum and Difference Method:

  • Let Eand E2 be the e.m.f.’s of the two cells to be compared by using the potentiometer. In this method both the cells whose e.m.f.s are to be compared are connected together.
  • When the two cells are connected in series such that negative terminal of one cell is connected to positive terminal of the other, then the two cells are said to assist each other and their resultant e.m.f. is given by sum of the e.m.f.s of the two cells. (E1 + E2)

Potentiometer 07

  • When the two cells are connected in series such that negative terminal of one cell is connected to negative terminal of the other, then the two cells are said to oppose each other and their resultant e.m.f. is given by the difference of the e.m.f.s of the two cells. ( E1 – E2)

Potentiometer 08

  • In the first step, the cells are connected to assist each other. The positive terminal of the combination of cells is connected to end A and another terminal is connected to jockey through galvanometer. By closing the key the jockey is moved along wire AB and null point P is determined such that galvanometer shows no deflection.  The length of wire AP = l1, is measured.  The p.d. across this length balances e.m.f. (E1 + E2)

∴  e.m.f. of the cell  = potential difference across AP.

E1 + E2  = K l1 . . . (1)

where K is the Potential gradient of the wire

  • In the second step, the cells are connected to oppose each other and procedure is repeated.

E1 – E2 = K l2  . . . (2)

Dividing equation  (1) by (2), we get,

Potentiometer 06

Thus knowing the values of l1 and l2 we can compare e.m.f.s of two cell.



To Find Internal Resistance of a Cell:

Potentiometer 11

  • A battery B having an e.m.f. greater than the e.m.f. (E) of the cell whose internal resistance (r) is to be measured, is connected in series with the potentiometer wire AB, a key K1 and a rheostat.
  • The positive terminal of the cell of e.m.f. E is connected to the end A of the potentiometer wire. The negative terminal of E is connected to a jockey through the galvanometer G. A  resistance box and a keyK2 are connected across the cell E.
  • Initially, the key K2 is kept open.  By closing the key K1 current is passed through the potentiometer wire so that uniform potential gradient is produced along the wire. By sliding the Jockey along the wire, a point of contact P1 for which the galvanometer shows zero deflection is found.  The length of the wire AP1 = l is measured. As the cell is in an open circuit, e.m.f. of the cell is equal to the p.d. across the length l, of the potentiometer wire.

E = K l          . . . (1)

Where K is the potential gradient of the wire.

  • Now a suitable resistance (R) is connected from the resistance box and the key Kis closed and once again null point P2 is found on the potentiometer wire.  The length AP= l1  is measured.  Let V be the terminal p.d. of the cell

Potentiometer 10

Thus knowing R, l and l1 we can calculate the value of r i.e. the internal resistance of the cell using this formula.



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