Cells, EMF , Internal resistance, Charging and discharging of cell, power of cell, practice problems, FAQs

Cells, or batteries as they are called, are used to run appliances daily. Remote controls, mobile phones, toy cars, are all able to function thanks to cells. You dismantle a toy and look carefully at its battery, you would notice there are two terminals; one positive( and the other negative

(). So what exactly does a cell provide that makes the above equipment function? The answer is electromotive force or emf. Imagine you took a battery, some connecting wires, and connected them to a bulb. You notice that the bulb glows. Why? The emf provided by the cell pushes charges from the positive terminal to the negative terminal, supplying current in the process. But do you think a cell has zero resistance? The answer is no. Almost each cell, when connected in a circuit, displays some resistance termed as its internal resistance. In this article, we shall explore cells, emf, internal resistance and how they are related.   

Table of contents

• Construction and working of a cell
• Emf, terminal voltage, internal resistance
• Charging and discharging of a circuit
• Power of cell
• Practice problems
• FAQs

Construction and working of a cell

A cell converts chemical energy to mechanical work. The longer end represents the terminal and the shorter end represents the terminal. The emf of a cell is defined as the work done( in pushing a charge through the entire circuit. This is possible due to chemical reactions occurring in the electrodes placed inside a cell. V across the battery = Emf in an open circuit, i.e when no electrical component like a bulb or resistor is connected to it.

Fig showing a cell

The unit of emf is volts. Its dimensional formula is

Emf, terminal voltage, internal resistance

The internal resistance arises due to resistance of the electrolyte inside the cell. It is measured in ohms  Terminal potential difference( comes into play when the circuit is closed by connecting a bulb or a resistor with it. Consider the following circuit where an external resistor is connected to the cell. The switch is closed. Then, 

 where current .

By Ohm’s law,

Note:

When no current flows in the circuit,i.e

Charging and discharging of a circuit

• When a battery discharges, it loses emf. Hence, the terminal voltage

  during discharge.

• When a cell charges, it acts as a load. Hence the terminal voltage

  during charging.

Power of cell

Power can be defined as the rate at which electrical energy is dissipated. If denotes output power delivered in a cell and is the current supplied by it, then

  since .

Let indicate the output power dissipated by the cell due to its internal resistance. Then 

Video explanation

Current electricity

Practice problems

Q. A battery having an emf of is connected to a resistor having resistance of . The current flowing in the circuit is . Find (i) terminal voltage (ii) internal resistance of the battery.

A. Given, current , ,

The terminal voltage across the resistor can be calculated as,                            

=

The internal resistance of the battery ,

Q. In the circuit below, find the potential difference between the points and

Solution) Current flowing in the circuit  

The voltage drop across resistor current resistance  

The voltage drop across resistor

sign indicates that current is flowing from to

Potential difference between the points and

Potential difference between points and

Q. The potential difference across the terminals of a battery is volts when there is no current flowing through the circuit. The potential difference falls to volts when a cell is connected to the external circuit and the current recorded is . Find the internal resistance of the cell.

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

A. a

When there is no current in the circuit, only emf is measured.

When the circuit is completed, terminal voltage,

Terminal voltage - internal resistance

Q. A cell of emf and internal resistance is connected in series with a resistor of resistance An ammeter of resistance is connected in series with the resistor, and it gives a reading of  Find ?

A.

Given , current

 Total resistance of the circuit

Now, current

FAQs

Q. How to decrease the internal resistance of a battery?
A. The internal resistance can be minimized by reducing the distance between the anode and the cathode.

Q. Which instrument is used to find the internal resistance of a cell?
A. Potentiometer, which is used to compare emf’s of two cells, is also used to find the internal resistance of a cell.

Q. Write the unit for internal resistance?
A. The unit of internal resistance is ohm

Q. Write the expression for current flowing in a circuit when a cell having internal resistance is connected in series with external resistor ?
A.

emf of the cell.