Alternating voltages and currents

The a.c. generator

 

Let a single turn coil be free to rotate at constant angular velocitysymmetricallybetween the poles of a magnet system as shown in FigureAn e.m.f. is generated in the coil (from Faraday’s Laws) which varies in magnitude and reverses its direction at regular intervals. The reason for  this is shown in Figure 14.2. In positions (a), (e) and (i) the conductors

and hence no e.m.f. is induced. In position (c) maximum flux is cut andhence maximum e.m.f. is induced. In position (g), maximum flux is cut and hence maximum e.m.f. is again induced. However, using Fleming’s right-hand rule, the induced e.m.f. is in the opposite direction to that in position (c) and is thus shown as E. In positions (b), (d), (f) and (h) some flux is cut and hence some e.m.f. is induced. If all such positions of the coil are considered, in one revolution of the coil, one cycle of  alternating e.m.f. is produced as shown. This is the principle of operation of the ac generator

 

The maximum power transfer theorem

The maximum power transfer theorem states

‘The power transferred from a supply source to a load is at its maximumwhen the resistance of the load is equal to the internal resistance of the source Hence, in Figure  when R = r the power transferred from the source to the load is a maximum

Norton’s theorem

Norton’s theorem states

‘The current that flows in any branch of a network is the same as that whichwould flow in the branch if it were connected across a source of electrical energy, the short-circuit current of which is equal to the current that would flow in a short-circuit across the branch, and the internal resistance which is of equal to the resistance which appears across the open-circuited branch terminals

* Norton’s theorem is summarized To determine the current flowing in a resistance R of a branch AB of an active network

(i) short-circuit branch AB

(ii) determine the short-circuit current ISC flowing in the branch

(iii) remove all sources of e.m.f. and replace them by their internal resistance or, if a current source exists,replace with an opencircuitthen determine the resistance r,‘looking-in’ at a break made, between A and B

(iv) determine the current I flowing in resistance R from the Norton equivalent network shown in Figure