# Critical Field Resistance & Critical Speed of DC Shunt Generator

## What is Critical Field Resistance of DC Shunt Generator ?

It is defined as the amount of field resistance required to generate emf in the armature winding. (or) The critical field resistance is defined as the field resistance of the generator which holds the rated voltage of it. (or) It is the value of field resistance beyond which the generator fails to build up the voltage if there is a further increase in the field resistance.

### Significance of Critical Field Resistance :

By the definition, it can be concluded that for a dc shunt generator to build up the voltage, the total field circuit resistance must be equal to or less than the critical field resistance value.

Run the machine as a shunt generator by connecting the field circuit to the armature terminals. It is to be noted that the only source of excitation for the dc shunt generator is the field current. But, at starting, it builds up voltage due to the presence of residual magnetism. This voltage causes a small current to flow through the field winding, resulting in the increase in flux per pole and hence the emf generated. Again, this emf causes some more current to flow through the winding and the same process continues till the equilibrium point is reached.

At the equilibrium point, the field resistance line intersects with the open-circuit characteristics curve, and at this point, the generator builds up the maximum voltage. It can be clearly understood by the figure below in which the O.C.C is drawn and some field resistances are taken.

In the above figure, the maximum emf corresponding to the field resistance R1 i.e., line 1 is E1. If the field resistance value is decreased so that the resistance line 2, becomes tangent to the O.C.C curve, then the maximum emf generated corresponding to this will be Ec. The value of resistance given by line 2, which is nothing but the slope of the line is called the critical field resistance.

If the value of field resistance is still decreased as represented by line 3, then the generator will not excite as there is no point of intersection existing between this line and the OCC curve. Hence, there is no emf induced in the generator beyond the critical field resistance.

## What is Critical Speed of DC Shunt Generator ?

Critical speed is defined as the speed at which the given shunt field resistance is equal to the critical resistance. It is the speed at which the shunt generator just fails to build up its voltage without any external resistance in the field circuit. It is denoted by Nc.

### Significance of Critical Speed :

If the speed of the dc machine is reduced to a value such that the field resistance line does not pass through the O.C.C then the machine fails to induce i.e., it may not generate any appreciable voltage. The speed at which the generator fails to build up the voltage is known as the critical speed.

Below this speed, the field resistance line does not cut the O.C.C. Hence fails to build up the voltage. Therefore the machine should not be operated below the critical speed as it fails to induce. Hence, it should always be operated above the critical speed.

### Determination of Critical Speed :

From the figure above, curve I is the O.C.C at a particular given speed N. OB is the tangent line to the O.C.C. OP is the line drawn to represent the given shunt field resistance. Curve II is the O.C.C drawn at the critical speed Nc to be determined. OP is the line tangent to the new O.C.C. If any ordinate AB is drawn intersecting line OP at C then,

#### Hence, to determine critical speed practically,Draw the given O.C.C and a line tangent to O.C.C.Draw a line ordinate intersecting the field resistance line and a tangent to O.C.C.Multiply the speed by the ratio of intercepts of ordinate drawn between field resistance line and the tangent line to O.C.C. Thus, the result will be the critical speed.

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