Difference Between Potentiometer And Meter Bridge, Important Topics For JEE Physics

Difference Between Potentiometer And Meter Bridge : A potentiometer and a meter bridge are both instruments used in electrical measurements, but they serve different purposes and operate in different ways. Wheatstone bridge can be used to find the value of unknown resistance. Using the working principle of the Wheatstone bridge we can operate a device named metre bridge. While A potentiometer can be used to compare the EMFs of two cells, find the internal resistance of a primary cell, and compare the resistances.

Metre Bridge In JEE Physics

Metre Bridge In JEE Physics : Metre Bridge In JEE Physics : Meter bridge is used to find the unknown resistance of a wire. The principle behind the working of metre bridge is Wheatstone bridge.

It consist of 1 m long uniform wire ( AB ), a known resistance ( R ) and an unknown resistance ( S ). A cell is connected across 1 m long wire and Galvanometer is connected between jockey and midpoint of R and S . Jockey is moved along the wire to obtain the balanced condition. Let the balance point is C and the length of AC is l cm. So, BC = (100 – l ) cm. Let r is the resistance per cm. Under balanced condition,

Potentiometer In JEE Physics

Potentiometer In JEE Physics : We know that resistance of an ideal voltmeter is infinite. But, practically voltmeter has a finite resistance. So, it draws some current. Hence, potentiometer is used to overcome this problem as it draws no current from the circuit. The working principle of potentiometer is “any unknown potential difference is balanced on a known potential difference which is uniformly distributed over entire length of potentiometer wire. This process is named as null deflection method.

The primary circuit of potentiometer consist of a constant source of voltage and rheostat. The secondary circuit consist of a galvanometer and cell of unknown emf.

Potential per unit length across potentiometer wire is equal to potential gradient.

i.e.,

So,

Where E is the emf of voltage source

R _P is the resistance of potentiometer wire

R ₁ is the resistance of rheostat

r is the internal resistance of cell.

Potential gradient ( x ) is an element of primary circuit and any charge in secondary circuit cases no charge in x .

Applications Of Potentiometer

(a) Comparison of emf of two cells

In the above setup, let the balancing length when 1 and 2 are connected is and the balancing length when 2 and 3 are connected is

So,

and

(b) Internal resistance of a given primary cell

We know that ...(1)

In the above circuit if key k is open

(where )

If key k is closed

(where )

Substituting these two relation in equation (1), we get

(c) Comparison of two resistance

In the above circuit, if 1 and 2 are connected and balanced

If 2 and 3 are connected and balanced,

Meter Bridge Example

Example 1 : A meter bridge is set-up as shown in figure, to determine an unknown resistance X using a standard 10 Ω resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are I cm and 2 cm respectively for the ends A and B . The determined value of X is

A. 10.2 Ω

B. 10.6 Ω

C. 10.8 Ω

D. 11.1 Ω

Sol. Using the concept of balanced Wheat stone bridge, we have,

Example 2: A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of EMF ε and internal resistance r . A cell C having emf and internal resistance 3 r is connected. The length AJ at which the galvanometer as shown in figure shows no deflection is

A. B.

C. D.

Sol. Given, length of potentiometer wire ( AB ) = L

Resistance of potentiometer wire ( AB ) = 12 r

EMF of cell D of potentiometer = ε

Internal resistance of cell ‘ D ’ = r

EMF of cell ‘ C ’ =

Internal resistance of cell ‘ C ’ = 3 r

Current in potentiometer wire

Potential drop across the balance length AJ of potentiometer wire is

(Resistance per unit length of potentiometer wire × length AJ )

where, x = balance length AJ .

As null point occurs at J so potential drop across balance length AJ = EMF of the cell ‘ C ’.