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Home Excitation Characteristics of IronCore Reactors Time Constant as Functions of Volume  
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Time Constant of Reactors as Functions of Volume
The time constant of an inductive circuit is defined as the ratio L/R where L is the inductance and R the resistance of the circuit and both L and R are assumed to be constant. If a reactor has an air gap in its core and the reluctance of the iron, hysteresis, and eddy currents are neglected, then the inductance is constant; and if the winding is at a constant temperature, its resistance is constant also. Consider, on that basis, an ironcore reactor with an air gap of length g as shown in Fig. 516. Let the effective crosssectional area of the air gap be A_{g} and the net area occupied by the conductors in the winding be k_{w}A_{w}, where k_{w} is a space factor and A_{w} is the area of the window in the core, i.e., the area of the space between the center leg and one outer leg of the core in Fig. 516. The space factor k_{w} is less than unity because not all of the window area A_{w} is occupied by conductor material of the winding since some space is occupied by electrical insulation and voids between turns, winding, and core.
When the reluctance of the iron and magnetic leakage are neglected, the selfinductance is, according to Eq. 411
where N is the number of turns in the reactor winding. The resistance of the winding, which is a conductor of uniform cross section, is given by
Where p is the resistivity of the conductor material, usually copper, l the length of the winding, and A the crosssectional area of the conductor material. The length is
Where l_{t} is the mean length of the turns and the area
From Eqs. 579, 580, and 581 it follows that the resistance of the winding is
so that the time constant
If all linear dimensions of the reactor core and air gap are increased by a factor k, the areas A_{w} and A_{g} are each increased by k^{2}, whereas the lengths l_{t} and g are increased directly as k, so that the time constant L/R for a given configuration of core and winding increases as k^{2} or as the 2/3 power of the volume, i.e.
It should be noted that the time constant is independent of the number of turns because the inductance and resistance of the winding both vary as the square of the turns for a given space factor k_{w}.


Home Excitation Characteristics of IronCore Reactors Time Constant as Functions of Volume 