Question

The potential difference in open circuit for a cell is $2.2\,V$ . When a $4\Omega$ resistor is connected between its electrodes the potential difference becomes $2\,V$ . The internal resistance of the cell will be:
A) $1\Omega$
B) $0.2\Omega$
C) $2.5\Omega$
D) $0.4\Omega$

Answer 1

Here we have to apply the relationship between internal resistance, emf, voltage and resistance to get the answer.
Internal resistance refers to the opposition to the current flow generated by the cells and batteries themselves, which contributes to heat generation. Internal resistance is calculated in ohms.

Internal resistance is where there is current present in the unit or electrical circuit and there is a voltage reduction in the source voltage or the source battery. It is caused by electrolytic materials in batteries or other sources of voltage.

Complete step by step solution:
First let us see what potential difference is-
The potential difference is the difference between two points in a circuit in the amount of energy that the charge carriers have.

Terminal potential difference- Terminal potential difference is usually found in cells or batteries.

The potential difference in a closed circuit between the two poles of a cell is called the cell’s terminal potential difference. When we measure the battery’s emf as we evaluate the potential difference between the terminals of a battery that is not a full circuit. This is the overall amount of work the battery can do to push charge from one terminal through the circuit to the other terminal per coulomb of charge.

Terminal voltage is mathematically represented by-
$V = emf - Ir$ ,
where $emf$ is the electromotive force,
$I$ is the current flowing,
and $r$ is the resistance.
Given,
Voltage, $V = 2V$
EMF, $E = 2.2V$
Resistance, $R = 4\Omega$
Internal resistance of the cell is given by:
$r = \dfrac{{E - V}} {V}R \\\ = \dfrac{{2.2 - 2}} {2} \times 4\Omega \\\ = 0.4\Omega \\\$

Hence, option D is the answer.

Note:
Here we have to be careful as to which the emf is and which value is the voltage. Also, when resistance is given in the question then only we need to use it otherwise it is not needed.