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# Critical Resistance of a DC Shunt Generator

## Critical Field Resistance of DC Shunt Generator

The critical field resistance (R_{C}) of a DC shunt generator is defined as the maximum field circuit resistance with which the shunt generator would just excite.

The voltage build-up in a shunt generator depends upon field circuit resistance. If the field circuit resistance is R_{1}, then the generator will build-up a voltage V_{0} (see the E_{0} versus If curve). If the field circuit resistance is increased to R_{2}, then the generator will build-up a voltage V_{0} slightly less than V_{0}. As the resistance of the field circuit is increased, the slope of the field resistance line also increases.

When the field resistance line becomes tangent (line OC) to magnetisation characteristics, the generator would just excite. Now, if the field circuit resistance is increased beyond this point (as line OD), then the generator will fail to excite. Therefore, the field circuit resistance represented by the line OC, which is tangent to the magnetisation curve is known as critical field resistance (R_{C}) of a shunt generator.

Therefore, a shunt generator will build up voltage only if the field circuit resistance is less than the critical field resistance.

## Critical External Resistance of a DC Shunt Generator

The minimum value of load resistance across the terminals of a shunt generator, which is required to excite the generator, is known as critical external resistance.

If the load resistance across the terminals of a shunt generator is decreased, then the load current increases. Although, there is a limit to the increase in the load current with the reduction of the load resistance.

Any reduction in the load resistance beyond this point, instead of increasing the current, results in the reduced load current. This is because on reducing load resistance, the load current momentarily increases and results in decrease of the terminal voltage due to armature reaction and IR drop. As a result of this, the external characteristics of the shunt generator turns back.

The tangent (line OA) to the curve represents the minimum value of external resistance for which the shunt generator excites on load and is known as critical external resistance.

If the external resistance is less than the critical external resistance, the machine will prohibit to excite or de-excite if already running.