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What are the basic differences between EMF and voltage? Is it that the voltage of a battery is EMF and voltage is a potential difference between two points?

Also, please give me some suggestions on how to take sign convention in Kirchoff's law etc.

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Very little

The terms voltage and emf are very closely related. Potential difference is another, very similar term. All three have subtly different meanings, and in some cases they are interchangeable, in others they are not. All three are measured in volts.

Potential difference is a measurement of the difference in energy per electron at different points in the circuit. It is always a relative measurement, so if the potential difference between two points on a circuit is 2V then each coulomb has 2J more energy at one point than the other. (A coulomb is just a fancy name for 6 billion billion electrons). Potential difference can be measured in several units, but the most common is volts, which is used in both metric and imperial systems.

emf stands for Electro Motive Force. It is a measure of the amount of energy added to a coulomb by something. If a battery has an emf of 2V, then it adds 2J to each coulomb flowing through it. If the battery is perfect, then that also means that the potential difference between the two ends is also 2V. If the battery is imperfect, then some of that extra energy may be lost again in the internal resistance of the battery. Changing magnetic fields also produce an emf in nearby wires. As above, it is almost always measured in volts in both metric and imperial systems.

Voltage is a less well-defined term. Sometimes the word voltage, or more often voltage across is used to mean a potential difference. Sometimes voltage is used to refer to an emf - especially when talking about batteries. The most common use is to refer to the potential difference between some point on the circuit and ground. Ground may be the same potential as the planet earth, or it may be some arbitrarily chosen point in the circuit. Voltage is always measured in volts.

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All Electromechanical devices that can move have EMF. This is a generator action of moving magnetic fields in coils.

The M stands for Motive meaning "in motion" or moving.

If you are applying voltage TO the device, EMF is the internal generated voltage that opposes when it speeds up thus the surge current torque also reduces. This surge current is limited only by the coil & cct. resistance or DCR and is often 10 to 25% or equivalent motor impedance at full load.

If the device does not move then it is just an inductor with resistance.

All DC motors are rated in V/Hz or kV/RPM for EMF which is the same as applied voltage (ignoring the conduction losses).

AC motors either operate in sync. or with limited slip or are series wound and spin as fast as it will commutate and still have torque.

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EMF stands for electromotive force. That's the basic physical phenomenon being discussed. One unit of measure of electromotive force is Volts.

In electronics, Volts is pretty much the only unit used to measure EMF in, so we take a shortcut and say "voltage", which really means "electromotive force in units of Volts".

For practical purposes in electronics, "EMF" and "voltage" mean the same thing. Technically "voltage" is more specific since it also includes the units that the physical quantity is being measured in.

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