A cell is a source of electric current in the electrical circuit. The Potential difference between terminals of a cell in an open circuit (when no current is drawn) is called electromotive force (emf) of the cell. When electrical circuit is closed and current is drawn from the terminal potential difference between two terminals is called terminal potential difference (v) of the cell. The cells can be connected in series as well as in parallel combinations. Like resistor cell also offers opposition to the flow of current. This opposition offered by cell is called internal resistance of the cell.
Three cells, each of emf \( \varepsilon \) and internal resistance \( r \) are connected with external resistor \( R \) as shown in fig. The value of current (\( i \)) flowing in the circuit will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{\varepsilon}{R + 3r} \)
The three cells are in series, but one of them is connected in reverse. In a series loop the emfs add with sign, while all the resistances simply add.
From the figure, the first and third cells have their long plate (positive terminal) on the left, while the middle cell has its long plate on the right, so the middle cell opposes the other two.
\( \varepsilon_{\mathrm{net}} = \varepsilon + \varepsilon - \varepsilon = \varepsilon \)
\( R_{\mathrm{total}} = R + r + r + r = R + 3r \)
\( \displaystyle i = \frac{\varepsilon_{\mathrm{net}}}{R_{\mathrm{total}}} = \frac{\varepsilon}{R + 3r} \)