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.
Two identical cells each of emf \( \varepsilon \) and internal resistance \( r \) when connected in series or in parallel across external resistance \( R \) give the same value of current. Then the relation between \( r \) and \( R \) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( r = R \)
The current from a combination of cells is the net emf divided by the total resistance of the circuit.
In series, the emfs add and the internal resistances add:
\( \displaystyle I_{s} = \frac{2\varepsilon}{R + 2r} \)
In parallel, two identical cells give the same emf \( \varepsilon \), and their internal resistances are in parallel, \( r/2 \):
\( \displaystyle I_{p} = \frac{\varepsilon}{R + r/2} = \frac{2\varepsilon}{2R + r} \)
Putting \( I_{s} = I_{p} \), the numerators are equal, so the denominators must be equal:
\( R + 2r = 2R + r \)
\( r = R \)