$($a$)$ A wire is carrying a direct current of $20$ A and a sinusoidal alternating current of peak value $20$A$.$ comment on the RMS value of the resultant current in the wire. $[$Understand$]$

$($b$)$ You are the transmitter specialist at an AM commercial radio station, which transmits at a frequency of $990$ kHz and an average power of $10$ kW $.$ As is the case for all commercial AM stations, the bandwidth for your station is $10$ kHz $.$ Your transmitter will radiate the power using a $50-$ antenna. The accompanying figure $1$ shows a simplified block diagram of the output stage of the transmitter. The antenna behaves exactly like a $50-$ resistor connected between the output of the amplifier and ground. You have been asked to identify the values of L and C so that the transmitter operates with the given specifications $[$Apply$]$

$[4$M$]$

Figure $1$

$($c$)$ As part of the calculations, simplify the above circuit to find the peak current that the inductor must handle and peak voltage across the capacitor. For your calculations, assume that the transmitted signal is a sinusoidal. $[$Analyze$]$

$[3$M$]$