Question

What is the potential difference between A and B?

Answer 1

Hint: The potential difference is defined as the energy required to send the unit electricity from one point to other point. Internal resistance of the cell or the battery is defined as the opposition made in flow of current from the cell or battery.

Formula used:
The formula of the ohm’s law is given by,
$ \Rightarrow V = I \times R$
Where the potential difference of the cell or battery is V, the current flowing from the circuit is I and the resistance on the circuit is R.

Complete step by step solution:
It is given in the problem that there is a circuit given and we need to find equivalent potential difference of the circuit.
First of all we need to find the equivalent resistance of the three resistances.
$ \Rightarrow \dfrac{1}{{{r_{eq.}}}} = \dfrac{1}{r} + \dfrac{1}{r} + \dfrac{1}{r}$
$ \Rightarrow \dfrac{1}{{{r_{eq.}}}} = \dfrac{3}{r}$
$ \Rightarrow {r_{eq.}} = \dfrac{r}{3}$
Now the two resistors are in parallel connection we get,
$ \Rightarrow \dfrac{1}{{{r_{eq.}}}} = \dfrac{3}{r} + \dfrac{1}{r}$
$ \Rightarrow \dfrac{1}{{{r_{eq.}}}} = \dfrac{4}{r}$
$ \Rightarrow {r_{eq.}} = \dfrac{r}{4}$.
Now the resistance of the equivalent external resistance and internal resistance are in series the equivalent resistance is equal to,
$ \Rightarrow R = r + \dfrac{r}{4}$
$ \Rightarrow R = \dfrac{{5r}}{4}\Omega $.
The formula of the ohm’s law is given by,
$ \Rightarrow V = I \times R$
Where the potential difference of the cell or battery is V, the current flowing from the circuit is I and the resistance on the circuit is R.
The ohm’s law is given by,
$ \Rightarrow V = I \times R$
$ \Rightarrow V = I \times \dfrac{{5r}}{4}$.

The potential difference between the points A and B is equal to $V = I \times \dfrac{{5r}}{4}$.

Note: The internal resistance also creates hurdles on the flow of the current and is also considered while solving the problem. The problem consists of resistors which are all connected in parallel to each other and equivalent resistance is connected to the internal resistor of the cell in series.