Page 850 - Basic Electrical Engineering

Figure 11.28 Phasor diagram showing the relationship between various quantities of an energy meter

The alternating flux ϕ will induce EMF E in the aluminum disc lagging
sc
se
ϕ by 90°. Similarly EMF induced by ϕ in the disc will be E . E will lag
sh
sh
sh
sc
ϕ by 90°. E will circulate eddy current i in the disc.
se
sc
sh
Similarly, E will circulate eddy current i in the disc.
sh
sh
Two opposite torques will be developed due to the interaction of ϕ with
sh
i and ϕ with i . From Fig. 11.28, it is noted that the angle between ϕ and
sh
sc
se
sh
i is ϕ and the angle between ϕ and i is (180 – ϕ).
sc
sh
sc
Average torque developed, T is
d

T ∝ [ϕ i cos ϕ − ϕ i cos(180° − ϕ)]
se sh
d
sh se
or,

T ∝ [ϕ i cos ϕ + ϕ i cosϕ]
d
se sh
sh se
Now, ϕ is proportional to V, i is proportional to I, and i is proportional to
sh
sh
sc
V, and ϕ is proportional to I.
se
Therefore,