The parameters of the apparatus that are important to itsfunction are: Solenoid winding: # turns N=1000; winding length Ls =10 cm; radius R=2.5 cm; wire radius r=0.05 mm; wire resistivity rs=2 x 10-8 Wm; length of the core extending above the solenoid Lc=10cm.
a Calculate the resistance and the inductive reactance of thesolenoid winding for its response when an applied e.m.f. of 110 Vr.m.s, 60 Hz is applied to it.
b Calculate the impedance of the solenoid winding, and the r.m.s.current that is induced to flow in it.
c Calculate the r.m.s. magnetic flux produced inside thesolenoid.
d Assume that the magnetic flux through the solenoid is channeledthrough the extended length of the steel rod core above thesolenoid, fringes radially along the length of that extended regionso that no flux leaves the top of the extended core. Calculate theradial field magnetic field in that region.
e Calculate the current that would be induced in the aluminum ringif it is located to surround the bottom of the extended region ofthe core. The parameters of the ring are: Length 4 cm, radialthickness 2 mm, resistivity rr= 3x10-8 Wm
f You close the switch long enough for the ring to be acceleratedvertically above the top of the extended core. Estimate how highabove the extended core it will travel before coming to a stop andfalling.
g Identify the parameters of the entire apparatus that determinehow high the ring will jump. Optimize the values for thoseparameters to make the ring jump to the maximum possible height.Assume the applied voltage and overall size of the apparatus cannotbe changed.
h If the solenoid has 1000 turns, how many turns should thesecondary have in order to apply 6 V across its terminals.
i The value of the capacitance C should be chosen so that it formsan LC circuit in series with the inductance of a 10-turn secondarywinding that is resonant at the 60 Hz frequency of the AC voltagethat is applied to the primary winding. What should be the value ofC?
