Transformers are extremely useful in power distribution. They allow us to transm

Question

Transformers are extremely useful in power distribution. They allow us to transmit power at very large AC voltages and very small AC currents, and then we can use a transformer to "step down" the voltage and "step up" the current at the point of use. To illustrate why this is beneficial, calculate the average power dissipated by 100 km of copper wire for (a) an rms voltage of 1.20 x 105 V and an rms current of 10-2 A, and (b) an rms voltage of 120 V and an rms current of 10 A. Assume the wire has a radius of 5.0 mm and a resistivity p = 20 n(ohms)m. (Hint: When finding the power that is dissipated in a circuit component, the relevant voltage is the voltage difference across that component.)

Explanation / Answer

R = rho * L/A =2 .54*e10

a) e-2*R*R = 2.54*e8J

b) 10*10*R*R= 2.54*e12J

so power in a is less than power in b by e4 times

where eN = 10^N

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