Question

Which of the following is true when the terminal potential difference of a cell is equal to the emf of the cell?
${\text{A}}{\text{.}}$ The cell is an open circuit
${\text{B}}{\text{.}}$ The internal resistance of the cell is zero
${\text{C}}{\text{.}}$ The load resistance R is much greater than the internal resistance r
${\text{D}}{\text{.}}$ All are true

Answer 1

Hint: Here, we will proceed by understanding why charge flows in a circuit. Then, we will be defining the term electromotive force (emf) in reference to terminal potential difference. Finally, we will be discussing the conditions for which the terminal potential difference of a cell will be equal to the emf of the cell.

Complete Step-by-Step solution:
When a circuit is connected and complete, charge can move through the circuit. Charge will not move unless there is a reason, a force to drive it round the circuit. Think of it as though charge is at rest and something has to push it along. This means that work needs to be done to make the charge move. A force acts on the charges, doing work, to make them move. The force is provided by the battery in the circuit.
A battery has the potential to drive charge round a closed circuit, the battery has potential energy that can be converted into electrical energy by doing work on the charge in the circuit to make it move.
The emf (electromotive force) is the potential difference between the terminals of a battery when no current is flowing through an external circuit when the circuit is open. Potential difference is the voltage across the terminals of the battery when the current is being drawn from it to an external.
The emf (electromotive force) is the maximum voltage that the battery can deliver whereas the magnitude of the potential difference is always less than the maximum possible value of emf. This is because of the internal resistance of the cell. But if the internal resistance of the cell is zero. Then, the potential difference between the terminals will equal to the emf (electromotive force).
Also, when the load resistance is much greater than the internal resistance then the internal resistance of the cell can be neglected (i.e., assumed zero). This will lead to the terminal potential of the cell equal to the emf (electromotive force) of the cell.
Therefore, all the options A, B and C represent the conditions for the terminal potential difference of the cell to be equal to the emf of the cell. All these options are true.

Hence, option D is correct.

Note- The electromotive force is induced in the electric, magnetic and gravitational field, whereas the potential difference is generated only in an electric field. The emf meter is used for measuring the electromotive force, whereas the voltmeter is used for measuring the potential difference.