Potentiometer

Potentiometer

In this topic we will discuss about Potentiometer,its working principle and its applications. Also we will know sensitivity of potentiometer.

Before to know about this topic student must read the following topics

i.- Kirchhoff’s law,to read this topic click here-

ii.- Wheatstone bridge,to read this topic click here-

iii.-Mete bridge,to read this topic click here-

Potentiometer – An instrument used to measure accurately the EMF or potential difference is called potentiometer.

Principle– Its working based on the principle that the potential drop across a conductor is directly proportional to the length of the conductor , if constant current passes through the conductor having uniform area of cross-section .

Construction –

 As we know ,

potential V=IR

V = (ρl/A) I

Since current is constant and area of cross-section is uniform  so V α l

Or V = K l

K = V/l ( K is a constant called potential gradient)

[ calculation of potential gradient ( students don’t have to derive it in case of potentiometer it is useful to solve  the numerical questions) – if Rh = r and resistance of the wire is r and E is the emf of  driver cell  then ,  current through the circuit is , i = E/ (R+r)

There fore potential difference at the end  the wire is v= i r

V= {E/ (R+r) } r . so potential gradient  K = V/l = {E/ (R+r) } r/l. ]

 

Application of potentiometer

  1. Determination of potential difference using potentiometer

All the arrangements are shown in the figure-

Let key K is closed then current i starts flowing through the circuit , if  RAB is the resistance of the wire then , We can write current i = ε/R+RAB ;

Now we close the key K1 also , in that case potential across the R1 is ‘V’ and null point J is at length ‘l’ as shown in figure .

Then V = Kl ;

But , K = VAB/ L   so we can write V =( VAB/ L)l   [L Is the total length of potentiometer wire]

Here VAB = i RAB = (ε/R+RAB)RAB ;

Therefore  V = [ {ε/(R+RAB)}l RAB]/L ;

  1. Comparison of emf of two cells –

A battery of emf ε is connected between the terminals A and B with variable resistance Rh , Now we have to compare the emf  ε1 and ε2 . We arrange the two cells having emf ε1 and ε2 as shown in figure . At first we connect the terminals 1 and 3 , let at that time J1 is the position where we grt null point , let length of A J1 is l1 so we can write  ε1= Kl1 ……….(i)

Again 1 and 3 is de-attached and terminal 2 and 3 is connected  now this time we get null point at J2 , let AJ= l2 . then we can write   ε2= Kl2 ………………….(ii)

Dividing equation (i) by equation (ii) we get  ,  ε1/ ε2= l1/l2 …………..req. eq.

Precautions of experiment-  (i) Current through the circuit must be constant .

(ii) the emf of the driving cell (ε) must be greater than emf of the cells whose value has to be compared .

  1. Determination of the internal resistance of the cell –

To find the internal resistance r  of the cell  emf ‘ε’ we setup the circuit as shown in figure.

Initially we close the switch ‘K’ and switch K2 is remain open .

In that case null point is at J1 , let AJ1=l1

Then we can write ε=Kl1………………(i)

Now the switch K1 is closed then the potential across the resistance R is   ‘V’ . And in that case we get the null point at J2 . And AJ2=l2

Then we can write V = Kl2   ………….(ii)

Dividing (i) by (ii) we get  ε/V = l1/l2 ……………(iii)

But we know that internal resistance of the cell   r = (ε-V /V)R = [ε/V-1]R ……….(iv)

And from equation (iii) and (iv) we get , r = [l1/l2 -1]R ………Req. Eq.

Sensitivity of potentiometer –

The sensitiveness of the potentiometer means the smallest potential difference which can be measured with the help of potentiometer .

The sensitiveness of the potentiometer can be increased ;

(i)by increasing the length of the wire of the potentiometer ,

(ii) by decreasing the value of potential gradient using reducing the current by increasing the resistance .

Difference between EMF of a cell and potential difference –

(i)  EMF -It is related with source of current

P.D. – It is related with any two points of the closed circuit.

(ii)  EMF – It cause of potential difference between two point of circuit .

P.D. – It is an effect .

(III)  EMF – It is the amount of work done in taking a unit charge once round the complete circuit .

P.D. – It is the amount of work done to bring unit charge from one point to another point .

(iv)  EMF – It is equal to sum of potential difference across all components of the circuit ( Including all          the cells connected  in the circuit .

P.D. – In a closed circuit the different components of the circuit have different potential difference .

(v)   EMF – It is independent of the external resistance and current drawn from the circuit .

P.D. – It depends on the resistance between two points of circuit and current flowing through it .

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