SOLVING PROBLEMS 19 and 20 April 19, 2010 Problem 19 (like 24.19): A Hertzian resonator has a capacitance of 1 pico-Farad and inductance of 1 micro-Henry. The spark gap breaks down at 10 kV and the resonator oscillates with an energy decay time of 5 microseconds. What is the frequency of the oscillation? What do you know? First of all, it doesn’t matter that it is Hertzian or Schmertzian. The angular frequency is 1 over the square root of L times C so the frequency is 2 10 1 2 1 9 LC f Hz = 159 MHz a) 159 MHz; b) 159 mHz; c) 159 kHz; d) 159 GHz; e) 159 Hz. What is the initial power being radiated? What do you know? The initial power will be the initial stored energy one half C V-squared, divided by the energy decay time or 10 10 10 10 2 5 8 12 2 CV P W. a) 10 W; b) 1 W; c) 1 mW; d) 10 kW; e) 1 W. Problem 20 (like 24.46): The polarization angles in stack of 9 perfect polarizing sheets are each set 10 O from the previous one to make a device for rotating the polarization by 90
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