   Next: Example 10.6: Impedance matching Up: Inductance Previous: Example 10.4: The RC

## Example 10.5: The step-up transformer

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