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** Up:** Inductance
** Previous:** Example 10.4: The RC

*Question:* An electric power plant produces GW of AC
electric power at a peak voltage of V. If it is desired to
transmit this power at a peak voltage of kV,
what is the appropriate turns-ratio of the step-up transformer?
What peak current would be sent over the transmission line if the peak
voltage were V? What peak current would be sent over the transmission
line if the peak
voltage were kV? What is the ratio of the ohmic powers losses in
the line in the two cases?

*Answer:* The appropriate turns-ratio
is

Since the peak power is given by , it follows that

Since the peak power remains unchanged after the signal
passes through the transformer (assuming that there are no
power losses in the transformer), we have

The ratio of the power lost to ohmic heating in the two
cases is

where is the resistance of the transmission line. Note that the ohmic
power loss is much greater at low peak voltage than at high peak voltage.

** Next:** Example 10.6: Impedance matching
** Up:** Inductance
** Previous:** Example 10.4: The RC
Richard Fitzpatrick
2007-07-14