Question

In a closed circuit, the emf and internal resistance of a battery are $E$ and $r$ respectively. If an external resistance $R$ is connected to the battery, the current flowing through the circuit shall be?
$A.{\text{ }}\dfrac{{Er}}{R}$
$B.{\text{ }}\dfrac{E}{{R + r}}$
$C.{\text{ }}\dfrac{E}{{rR}}$
$D.{\text{ }}\dfrac{{ER}}{r}$

Answer 1

Consider a closed circuit the emf and the internal resistance of a battery are $E$ and $r$ respectively connected, and an external resistance $R$ is connected to the battery. When the current is flowing to the circuit. So we can use the ohm’s law statement to find out the current flowing through the circuit.

Complete step by step answer:
Ohm’s law statement is written as,
Ohm’s Law states that current$(I)$ is flowing through a conductor is directly proportional to the voltage applied V across it,
$i.e,$ ${\text{V}} \propto {\text{I}}$
Simply,$V = IR$
Where $R$ is a constant of proportionality called resistance, which defines the resistance offered by the material of the conductor to the flow of current through it.
Total Resistance offered by a conductor to the flow of electric current depends on its length, area of cross-section and resistivity of the conductor.
$V =$ Voltage,
$I =$Current,
$R =$ Resistance,
The circuit will be like this:

Total resistance of circuit $= R + r$
$V = IR$
let us divide $R$ on both side we get,
$I = \dfrac{V}{R}$
Here we can write it as, we get
$\Rightarrow I = \dfrac{E}{{R + r}}$

Hence, the correct answer is option (B).

Additional information:
The current voltage, we can write as in the ratio form $\dfrac{V}{I}$ it remains constant and also a graph is must be a straight line is between the potential difference $V$ and the current $(I)$
In determining either voltage, current or impedance or resistance of a linear electric circuit, when the other two quantities are known, ohm's law. It also makes power calculation simpler.

Note: From the equation $\Rightarrow I = \dfrac{E}{{R + r}}$
We get, $V = E - IR$ - in this equation the term $V$ is called the potential of the cell. Clearly, the value of $V$ is less than that of $E$ . That means, the emf of the cell can not be gained as the total potential of the cell. The potential of amount $(Ir)$ is lost internally for the internal resistance $(r)$ of the cell. This is called the Internal Potential drop or Lost Volt.
In the equation $V = E - IR$, if the value of $(r)$ is very large then the value of $V$ becomes lesser and the value of $(Ir)$ becomes equal to the value of $E$. In that case, the cell can not produce potential in the outer circuit.