Question

In a closed circuit the emf is always;
A) Less that PD.
B) More than PD
C) Half the PD
D) Double the PD

Answer 1

The electromotive force (emf) is a force that drives an electron in the circuit, however the potential difference in a circuit is caused due to a battery, and so there is some work inside the battery.

Complete step by step solution:
What is EMF?
In electromagnetism and electronics, electromotive force (EMF), is the electrical action produced by a non-electrical source. Devices provide an emf by converting other forms of energy into electrical energy, such as batteries or generators. Sometimes an analogy to water pressure is used to describe electromotive force.

In electromagnetic induction, emf can be defined around a closed loop of conductor as the electromagnetic work that would be done on an electric charge (an electron in this instance) if it travels once around the loop. For a time-varying magnetic flux linking a loop, the electric potential's scalar field is not defined due to a circulating electric vector field, but an emf nevertheless does work that can be measured as a virtual electric potential around the loop.

A source of emf can be thought of as a kind of charge pump that acts to move positive charges from a point of low potential through its interior to a point of high potential. By chemical, mechanical or other means, the source of emf performs work $dW$ on that charge to move it to the high-potential terminal.

The emf $\varepsilon$ of the source is defined as the work $dW$ done per charge $dq$.
Hence, $\varepsilon$ = $\dfrac{{dW}}{{dq}}$.

What is the ‘potential’ difference in a closed circuit?
Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points, which is defined as the work needed per unit of charge to move a test charge between the two points. Electric potential differences between points can be caused by electric charge, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. A voltmeter can be used to measure the voltage (potential difference) between two points in a system; often a common reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy (electromotive force) or lost, used, or stored energy (potential drop).

Mathematically we can define voltage as;
${V_{x,y}} = \int\limits_x^y {Edl}$.
The EMF is always more than voltage. When a cell is in closed circuit, i.e., when current is drawn from it, then the potential difference between its electrodes is called the terminal voltage. It is always less than the e.m.f. because when charge flows in a circuit, some energy is spent in the flow of charge through the electrolyte of the cell.

Hence option (B) is correct.

Note:
1. The voltage is only caused in an electric field.
2. EMF is caused in the gravitational field, magnetic field and electric field.