Homework question Suppose you wanted to build a circuit that would oscillate at 10,000 Hz (10 kHz) by employing a capacitor and an inductor in series. Being a experimenter with physics, you open your parts drawer and find a capacitor that is marked 1 f which you figure is a good start. But, all you have now is a spool of wire with which to make a solenoid to provide the inductance. 1. What inductance do you need to make the circuit oscillate at 10 kHz if the capacitor is connected with a little charge on it at first? 2. Find a solution for the coil's length, assuming you have a 10 meter long piece of wire to make it. Your text discusses this and shows that the self-inductance of a solenoid is L = 4kmN2A/l The SI unit for inductance is the henry (H). N is the number of turns, A is the cross sectional area of the coil, and l is its length. (Hint: The area is r where r is the radius of the coil. The circumference of the coil is 2r. If there are N turns around it, you can find the total length of the wire.) 3. If there is no resistance, the circuit will oscillate naturally. What is the critical resistance above which the circuit will not oscillate because the resistance dampens the oscillations? 4. What would be the consequence of using very fine wire of small diameter for the coil rather than larger diameter wire? Explain your answers in your own words, and, as always, if you use source to help you answer it you should cite your reference.