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Electromotive Force

No current flows in a copper wire by itself, just as water in a horizontal tube does not flow. If one end of the tube is connected to a tank with water such that there is a pressure difference between the two ends of the horizontal tube, water flows out of the other end at a steady rate. The rate at which water flows out depends on the pressure difference, for a given tube. If the flow rate (current) is to be kept constant, the water flowing out for instance has to be put back into the jar to maintain the pressure head. This requires work to be done by an external agency.

The above analogy brings out several features of electrical current flow. An electric current flows across a conductor only if there is an electric potential difference between its two ends. To maintain a steady current flow, one needs an agency, which does work on the charges. This agency is called the Electromotive Force or emf.

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Electromotive Force Definition

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Current always flows in the closed circuit. When a closed circuit (copper wire) is connected with a source of electromotive force, the electromotive force directs the electric charges to flow in a uniform direction which constitutes the current. Source of electric charge can be batteries of generators.

Emf can be considered as a charge pump. When emf source is connected between the two ends of the conductor it directs the charges to move from the region of lower potential to the region of higher potential.
Electromotive force can be defined as the work done per unit of charge. SI unit of Electromotive force is Volt.
For instance, in the Figure 1. shown below a resistor is connected to the source of energy, here battery. Consider that the wires which are connecting the resistor and battery are not offering any resistance to the flow of current. Battery has two terminals - Positive terminal and negative terminal. Positive terminal is at higher potential energy as compared to the negative terminal.

Electromotive Force

Now, if we neglect the internal resistance of the battery, there is potential difference across the battery.Terminal voltage of battery is equal to its electromotive force .But in practical situations there would always be some internal resistance of the battery, whenever there is current flowing in the circuit.

Kirchhoff's Law

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Kirchhoff states two laws which are very useful to solve the statistics of the circuits.

1) Kirchhoff's Junction Rule

Kirchhoff first Law deal with current in a closed circuit.

The algebraic sum of the currents at a junction in a closed circuit is zero.

Kirchhoff's Junction Rule

Therefore, I1 + I4 = I2 + I3 + I5

Hence, I1 + I4 - I2 - I3 - I5 = 0

or SI = 0

Sum of currents entering a junction = Sum of currents leaving the junction.
This rule is based on the fact that charge cannot be accumulated at any point in a conductor in a steady situation.

2) Kirchhoff's Loop Rule

The algebraic sum of the potential differences in any loop including those associated with emfs and those of resistive elements must be equal to zero.

$\sum V = 0$, (valid for any loop)

This rule is based on energy conservation, i.e., the net change in the energy of a charge after completing the closed path is zero. Otherwise, one can continuously gain energy by circulating charge in a particular direction.

The number of independent equations required to be obtained from the two Laws are equal to the number of currents which are unknown in the circuit. This is true in generally in most of the circuits.

Electromotive Force Equation

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In the Figure shown below, a battery with electromotive force E is connected with a resistance R. Let the internal resistance of the battery be r. Here the battery is connected with the resistance in R. Imagine that we are moving in clockwise direction from the point a to b in the circuit shown in Figure below. While moving from fro one point of the battery to the other end (here a to b) we will note the potential at various points in the circuit.

Electromotive Force Equation

When we start moving from a to b:
  1. First negative terminal of the battery comes. When we move from the negative terminal of the emf source (battery) to the positive terminal of the battery, potential will increase by E.
  2. After that, resistance r (internal resistance of the battery) is connected. If current I is flowing through the circuit then potential equals to Ir will be dropped across r.
Therefore the terminal voltage across the battery would be : $E–Ir$
Where E is the Open circuit voltage across the battery terminals when no current is flowing in the circuit.

From the diagram we can conclude that terminal voltage across the battery terminals will be equal to the potential across the resistance R.


$E – Ir$ = $IR$

$E$ = $I(R + r)$ ....(1)

Solving for E gives $E$ = $I(R + r)$

Solving for the current flowing in the circuit gives:

$I$ = $\frac{E}{R + r}$

Now in the Eqn.(1), if we multiply it by 'I' current. Then we get

$EI$ = $I^{2}R + I^{2}r$
Therefore, Power delivered by the battery is equal to the Power dissipated in the external resistance R and internal resistance of the battery. Therefore maximum power will be delivered to the load connected to the battery if r<< R.

Counter Electromotive Force

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Counter Electromotive Force is also called as the Back Electromotive force. To explain this we will first explain the principle of Self Induction.

Here we will differentiate the Electromotive forces and currents which are generated by the batteries etc. and electromotive forces which are due to change in the magnetic fields. Source emf and source currents be the emf and current which are generated by battery etc. and induces emf and induced current induced by the change in Magnetic fields.

Consider again the circuit shown in which Resistor, switch and source of emf are connected. When switch is closed, the current starts from zero but it does not reach to its maximum value immediately. According to Faradays law of the electromagnetic induction, as the source current increases, the magnetic flux associated with the current in the circuit loop also increases with time. As the magnetic flux increases with time, it results in induced electromotive force. flux creates an induced emf in the circuit. Induced emf in the circuit opposes the change in magnetic flux due to the change in source magnetic field. That is, the direction of the induced current is opposite to the source emf. That is why source current does not reach to its maximum value from zero immediately but there is a gradual increase in the source current with time.

This principle is called as the self-induction principle. This is due to the change in the source magnetic flux in the circuit because of which emf gets induced in the circuit. The emf induced is called a self-induced emf. It is also called as Counter Electromotive Force or Back emf. It is always proportional equal to the time rate change of the source current.

$E_{L}$ =$-L$$\frac{dI}{dt}$
Where $\frac{dI}{dt}$ is the rate of change of source current. L is inductance and SI unit of the inductance is Henry.

Resistance opposes to the flow of current and inductance gives opposition to the flow of inductance.
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