Potentiometer, measurement of internal resistance, comparison of two cells’ emf, Practice problems, FAQs

Cells, also known as batteries, supply current. You go to a hardware store and purchase a battery. You flip it over and look carefully at it, it has a certain reading that goes like “ or Now what does this mean? denotes volts; it is the unit for measuring emf or electromotive force of the cell. This emf() is responsible for the current that flows through when the circuit is closed by connecting wires and an electrical appliance. The work done by emf moves charges from one terminal of the battery to another. But do you think cells have zero resistance that allow them to supply the complete emf written on them? The answer is no. In other words, due to the chemical reactions occurring not so efficiently, the cell has a small value of internal resistance (In order to measure the emf and internal resistance of cells, a device called potentiometer is used. 

Table of contents

• What is a potentiometer?
• Principle and construction of a potentiometer
• Comparison of emf of 2 cells using potentiometer
• Measurement of internal resistance of a cell using potentiometer
• Practice problems
• FAQs

What is a potentiometer?

A potentiometer is a device used to measure the internal resistance of a cell or compare the emf of two cells. It does not draw any current from the cell to measure the potential difference. In this aspect, it resembles an ideal voltmeter, which is said to have infinite resistance; meaning it does not draw any current from the circuit. The following diagram shows a potentiometer; it has a primary circuit with a wire clamped between copper strips. It is made of alloys like constantan or manganin which have high resistivity and low temperature coefficient of resistance; this means that their resistance does not vary greatly with temperature. A sliding contact named jockey can be moved from one end to the other end of the wire . A variable resistance is connected in series with a key, a cell of emf One end of the jockey is connected to a galvanometer which detects flow of current through the circuit.

Principle and construction of a potentiometer

Potentiometer works on the following principle: When a constant current is passed through a wire whose cross sectional area is uniform, then the potential drop or difference across a portion of the wire is proportional to its length. Let be the length of the wire and indicate its resistivity. 

Then its resistance  

The potential difference across this portion, 

is called the potential gradient of the wire.

The wire is of usually in length. Let indicate the resistance of the wire. The ends and are connected to the cell On closing the switch the current starts flowing in the circuit, 

Upon moving the jockey, a point is reached where there is null deflection, i.e. no current flows through the galvanometer. When this happens, the potential difference across points and will be equal to that of between the points and

Comparison of emf of 2 cells using potentiometer

Let us consider two cells having emf’s and connected across the points and Two keys and are connected in series with and respectively. The switch is closed, the balancing length is noted. When is attained, the galvanometer shows zero deflection. 

By the principle of potentiometer we have, 

Now upon closing , cell is included in the circuit. The balancing length is now  

From equations and

Measurement of internal resistance of a cell using potentiometer

Consider a cell whose internal resistance is and emf It is connected with the potentiometer and the switch is kept open. is the external resistance. The jockey is slid till there is no deflection. Let the balancing length be Then 

Now the switch is closed and the current flowing in the lower branch is

If indicates the terminal potential difference across the cell (when is taken into account), then is the balancing length corresponding to the closed circuit. But  

Equating, we get 

Diving equations and , we get 

Also,

Practice problems

Q1. The wire of a potentiometer is long and has a resistance of A cell having internal resistance of and emf is connected in series with it. Calculate the potential gradient along the wire. 

Answer. Given, length of the wire  
Current flowing in the circuit,. 

Now voltage drop across the wire

Q2. In a potentiometer experiment, the cell is found to be balanced against and of wire respectively when it is not short circuited and short circuited through an external resistance of connected in series with it. Find the internal resistance of the cell.

(a) (b) (c) (d)

Answer. a 

Given,

,

Q3. In a potentiometer experiment, a cell having an emf value of gives a balancing point of If it is replaced by another cell, the balancing point is observed to be Find the emf of the unknown cell.

(a) (b) (c) (d) None

Answer. c 

Let be the emf of the first cell. Then is its corresponding balancing length.

Let be emf of the second cell. Then indicates the balancing length corresponding to the second cell. 

The ratio of the emfs is equal to the ratio of the corresponding balancing lengths.

,

=

Q4. A potentiometer wire of length has a resistance of It is connected in series with a cell of emf and a resistor R. A source of emf is balanced against a length of of the potentiometer wire. What is the value of R? 

(a) (b) (c) (d)

Answer. a

Given

Let be the resistance of the portion of the wire which is balanced against the cell.

Then the current flowing through the potentiometer wire would be 

FAQs

Q1. What are the four types of potentiometers?
Answer.  Rotary, linear, concentric and multi turn slide potentiometers are different types of potentiometers.

Q2. Do potentiometers use magnets?
Answer.  Yes, the magnetic membrane utilizes a magnetic field that is used for contactless connection.

Q3. What are the errors occurring in potentiometer?
Answer. 
1) The wire must be kept taut, otherwise the balancing length cannot be measured accurately. 
2) Jockey being slid on the wire instead of tapping it which gives wrong reading due to friction. 

Q4. Can an EMF greater than the EMF of the main circuit be balanced by a potentiometer wire?
Answer. No, there will not be any null point if EMF is greater than the EMF of the main circuit.