If a Cardew voltmeter be placed on an alternating circuit in which the volts are oscillating between maxima of +100 and -100 volts, it will read 70.7 volts, though the arithmetical mean is really only 63.7; and 70.7 steady volts would be required to produce an equal reading.
Fig. 1,237.—Diagram illustrating virtual and effective pressure. If the coil be short circuited by the switch and a constant virtual pressure be impressed on the circuit, the whole of the impressed pressure will be effective in causing current to flow around the circuit. In this case the virtual and effective pressures will be equal. If the coil be switched into circuit, the reverse pressure due to self induction will oppose the virtual pressure; hence, the effective pressure (which is the difference between the virtual and reverse pressures) will be reduced, the virtual or impressed pressure remaining constant all the time. A virtual current is that indicated by an ammeter regardless of the phase relation between current and pressure. An effective current is that indicated by an ammeter when the current is in phase with the pressure. In practice, the current is hardly ever in phase with the pressure, usually lagging, though sometimes leading in phase. Now the greater this phase difference, either way, the less is the power of a given virtual current to do work. With respect to this feature, effective current may be defined as: that proportion of a given virtual current which can do useful work. If there be no phase difference, then effective current is equal to virtual current.
The matter may be looked at in a different way. If an alternating current is to produce in a given wire the same amount of effect as a continuous current of 100 amperes, since the alternating current goes down to zero twice in each period, it is clear that it must at some point in the period rise to a maximum greater than 100 amperes. How much greater must the maximum be? The answer is that, if it undulate up and down with a pure wave form, its maximum must be √2 times as great as the virtual mean; or conversely the virtual amperes will be equal to the maximum divided by √2. In fact, to produce equal effect, the equivalent direct current will be a kind of mean between the maximum and the zero value of the alternating current; but it must not be the arithmetical mean, nor the geometrical mean, nor the harmonic mean, but the quadratic mean; that is, it will be the square root of the mean of the squares of all the instantaneous values between zero and maximum.
Effective Volts and Amperes.—Virtual pressure, although already explained, may be further defined as the pressure impressed on a circuit. Now, in nearly all circuits the impressed or virtual pressure meets with an opposing pressure due to inductance and hence the effective pressure is something less than the virtual, being defined as that pressure which is available for driving electricity around the circuit, or for doing work. The difference between virtual and effective pressure is illustrated in fig. 1,237.
Ques. Does a given alternating voltage affect the insulation of the circuit differently than a direct pressure of the same value?
Ans. It puts more strain on the insulation in the same proportion as the maximum pressure exceeds the virtual pressure.
Fig. 1,238.—Current or pressure curve illustrating form factor. It is simply the virtual value divided by the average value. For a sine wave the virtual value is 1 / √2 times the maximum, and the average is 2 / π times the maximum, so that the form factor is π/2√2 or 1.11. The induction wave which generates an alternating pressure wave has a maximum value proportional to the area, that is, to the average value of the pressure wave. Hence the induction values corresponding to two pressure waves whose virtual values are equal, will be inversely proportional to their form factors. This is illustrated by the fact that a peaked wave causes less hysteresis loss in a transformer core than a flat topped wave, owing to the higher form factor of the peaked wave. See wave forms, figs. 1,245 to 1,248.