Week 9: Alternating Current Circuits 339
Problem 7.
V 0V 0V 0RRRtRtloadloadV 1In this problem you must analyze the problem of power transmission that dominated the famous
Edison vs Tesla “war” that took place some hundred years ago. Above you can see two alterntives
for transmitting power long distances. The first circuit is Tesla’s – generate AC power at a relatively
low voltageV 0 (which is easy). Step the power up to a very high voltageV 1 ≫V 0 and transmit it
at high voltage across a long transmission wire of fixed resistanceRt. Step it back down to voltage
V 0 and then place the loadRloadacross it.
The second circuit is Edison’s. Generate a DC voltageV 0. Transmit it down identical transmis-
sion lines and place it across an identical load.
Your job is tocompute the way the power is divided upbetweenPload(which is fixed – the power
we need to light a light bulb, for example) andPt, the power wasted heating up the transmission
lines. The better solution hasPt≪Pload. Find a relationship between the ratios:
V 0
V 1and
Pt
Pload
that proves that Tesla’s solution wins (and by how much it wins, given “reasonable” estimates for
Rt/Rload).
Problem 8.
L C RI(t)V cos( t)o ωAparallelLRC circuit connected across a variable AC voltage sourceV=V 0 cos(ωt) is drawn
above. Find:
a) The currentI(t) in the primary supply wire (as shown in the figure above) with all terms, e.g.
the phaseδ, and the impedanceZdefined (the latter in terms of the individual reactances).
b) Theaveragepower dissipated by the circuit. Note that (if you are clever and remember what
each elements does in the circuit) you don’t reallyhaveto solve a) to get this answer, although you
can certainly get the same answer from a knowledge ofV(t) andI(t) and some integration.
Hint: To find the answer you must add thecurrentsbeing drawn by each element separately!