Question

-In a closed circuit the e.m.f. and internal resistance of the generator are E and r respectively. If the external resistance in the circuit is R, then the Ohm's law has the form:
A. $I = \dfrac{E}{{\left( {R + r} \right)}}$
B. $I = \dfrac{E}{r}$
C. $I = \dfrac{E}{r}$
D. $I = \dfrac{E}{{R - r}}$

Answer 1

Hint: To solve this question we use Ohm’s law. In this question, two resistances are used in the closed circuit that is internal resistance and external resistance. We have to know the term internal resistance. It is the resistance within a voltage source that causes a reduction in the source voltage in the presence of current. And external resistance is the restriction to the flow of electricity.

Complete step by step answer:
We know that the relation between the voltage current and resistance is given by Ohm’s law. So, according to Ohm’s law, the electric current that is moving within a conductor is directly related to the potential difference across it, and the proportionality constant is the resistance of the conductor.
Mathematically, Ohm’s law can be written as,
$V = IR$
Here, $V$ is the potential difference, $I$ is the current and $R$ is the resistance.
The potential difference becomes emf if no current flows in the circuit.
Therefore, the expression becomes,
$E = IR$
Also, we have to know the term EMF. It is the amount of energy given by the battery to each charge passing through it.
It is given in the question that the circuit is closed and the emf and internal resistance of the generator are E and r respectively.
So, the internal and external resistance are added together.
Therefore, the Ohm’ law can be written as
$
E = IR'\\
\implies E = I\left( {R + r} \right)\\
\implies I = \dfrac{E}{{\left( {R + r} \right)}}
$

Therefore, the correct option is (A).

Note:
In this question, we have to know the formula of Ohm’s law and the terms, internal resistance and external resistance. Both the resistance are added when we use Ohm’s law because they are present as a closed circuit.