Flux and Average Voltage

If the variables are separated in equation 1, thus

an expression for flux may be found :

Now if we consider the time interval 0 to π/ω, we have

[9]

Equation 9 gives the relation between maximum flux and the time integral of voltage. The left side of the equation is the area under the voltage-time wave. For a given frequency, it is proportional to the average voltage value. This is perfectly general and holds true regardless of wave form. If the voltage wave form is alternating, the average value of the time integral over a long period of time is zero. If the voltage wave form is sinusoidal, the flux wave form is also sinusoidal but is displaced 90° as in Fig. 5, and the integral over a half-cycle is

whence

[10]

Equation 10 is the relation between maximum flux, effective voltage, frequency, and turns. It is a transposed form of equation 4.