Answer to Question 10

 

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A transmitter is connected to the aerial by a thick cable that is 5.0 mm in diameter. The transmitter operates at a frequency of 200 kHz. The cable is made from aluminium, which has a resistivity of 2.82 10-8 W m. Show that the depth of the layer that carries 63 % of the current is about 0.2 mm.

Formula:

m = 1.0 4p 10-7 H = 1.26 10-6 H m-1

w = 2 p 200 000 Hz = 1.26 106 rad s-1

d = [(2 2.82 10-8 W m) (1.26 106 rad s-1 1.26 10-6 H m-1)]0.5 = 1.9 10-4 m = 190 mm (which is about 0.2 mm)