1. EMF

Electromotive Force 

The electromotive force, E of a cell is defined as the total work done in driving one coulomb of charge round a circuit.

Electromotive force is the energy per unit charge supplied by a source of electrical energy, such as a battery or a generator. It is not actually a force, but rather a potential difference between two points in an electric circuit. Electromotive force is measured in volts.

                        e.m.f  = work/charge = W/Q

            where W is measured in joules, Q in coulombs, e.m.f in volts. Hence

                                    V = W/Q

                        or         W = QV

Electromotive force can be used to describe the voltage supplied by a battery or generator, and it is related to the internal workings of these devices. For example, in a battery, the e.m.f is created by a chemical reaction that separates charges and creates a potential difference between the terminals of the battery. In a generator, the e.m.f is created by the relative motion between the magnetic field and a conductor.

4.1.1 Internal resistance

The internal resistance, r is the opposition to charge flow offered by the cell when it is discharging current to a circuit.

Internal resistance is the inherent resistance within an electrical source, such as a battery or generator, that opposes the flow of current in an electric circuit. It is caused by the resistance of the materials used to construct the source, as well as the resistance of the chemical reactions that occur within the source.

Internal resistance is important because it affects the output voltage and current of the source. As current flows through the source, it encounters resistance, which causes a voltage drop across the source. This reduces the output voltage and current of the source, and the amount of reduction depends on the internal resistance of the source.

4.1.2 Voltage drop

Voltage drop is the reduction in electrical potential that occurs when current flows through a component or conductor in an electric circuit. It is caused by the internal resistance of the component, which converts some of the electrical energy into heat. The voltage drop is proportional to the current flowing through the conductor and internal resistance of the conductor.

                                    v = Ir

e.m.f = p.d across external resistance + p.d across internal resistance

            E = V + v

Applying Ohms law, we have

            E = IR + Ir

            E = I (R+r)

            I = E/(R+r)

4.1.3 Examples

1. A battery of e.m.f 24V and internal resistance 4Ω is connected to a resistor of 32Ω. What is the terminal p.d of the battery?

2. A cell of e.m.f 1.5V is connected in series with a resistor of resistance 3Ω. A high resistance voltmeter connected across the cell registers only 0.9V. Calculate the internal resistance of the cell.

3. An electric bell takes a current of 0.2A from a battery of two dry cells connected in series. Each cell has an e.m.f of 1.5V and an internal resistance of 1.0Ω.

(i) Calculate the effective resistance of the bell.

(ii) What current would the bells take if the cells were arranged in parallel?

4.2 Electrical Work Done in a Circuit

Work is done when charges flow from one point to another of different potential in a circuit. If Q coulombs of electricity flows between the two points whose differences in potential is V volts, then work done(W) is given by

                                    W = QV

                                    (joules = coulomb x volts)

            The quantity of charges Q coulombs is given by

                                    Q = It

            where I is the current in amperes and t is time of flow of current in seconds

                                    W = QV = IVt

                                    W = IVt

                                    (joules = amps x volt x seconds)

            But from Ohms law, V = IR

                                    W = QV = IVt = I x IR x t

                                                = I2Rt

                                    W = I2Rt

                        Substituting I = V/R

                                    W = V2t/R

Magnetic Flux:

Magnetic Flux through a surface is the total number of magnetic field lines passing through it. If B = magnetic field strength, A = Area and  = angle between the normal the surface:

= BACos

Unit = Weber(wb/m2)

Note Flux changes when; B changes (field strength varies), A changes (loops size and shape), and  changes (loops rotate in the field)