Question

Question 4 4 pts Hint: This question tests on Section 31.2. The receiving antenna for a radio is a long cylinder of iron with wire wrapped around it. The inductance of this antenna, which is part of the radio's circuitry, is 1.13 mH. Suppose the maximum current in the radio's RLC circuit needs to be 2.817 mA when the voltage across the inductor is 1.20 Volts. What is the necessary linear (not angular) frequency? Express your answer in kilo-hertz using the format ## (a two digit number with no decimal point).

Answer 1

Maximum current, I₀ = 2.817 mA

The voltage across the inductor, V_L = 1.20 V

Inductive reactance, X_L =( V_L / I₀ ) = ( 1.20 / (2.187 X10^-3)) = 548.696 ohms

Angular frequency, w = ( X_L / L ) = ( 548.696 / (1.13 X10^-3)) = 485572.43 rad/s

Linear frequency, f = (w / (2*pi)) = (485572.43 / (2*pi)) = 77281.25 Hz = 77.281 kHz = 77 kHz (Ans)