The parameters of the apparatus that are important to its function are: Solenoid winding: # turns...

The parameters of the apparatus that are important to its function 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=10 cm.
a Calculate the resistance and the inductive reactance of the solenoid winding for its response when an applied e.m.f. of 110 V r.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 the solenoid.
d Assume that the magnetic flux through the solenoid is channeled through the extended length of the steel rod core above the solenoid, fringes radially along the length of that extended region so that no flux leaves the top of the extended core. Calculate the radial field magnetic field in that region.
e Calculate the current that would be induced in the aluminum ring if it is located to surround the bottom of the extended region of the core. The parameters of the ring are: Length 4 cm, radial thickness 2 mm, resistivity rr= 3x10-8 Wm
f You close the switch long enough for the ring to be accelerated vertically above the top of the extended core. Estimate how high above the extended core it will travel before coming to a stop and falling.
g Identify the parameters of the entire apparatus that determine how high the ring will jump. Optimize the values for those parameters to make the ring jump to the maximum possible height. Assume the applied voltage and overall size of the apparatus cannot be changed.
h If the solenoid has 1000 turns, how many turns should the secondary have in order to apply 6 V across its terminals.
i The value of the capacitance C should be chosen so that it forms an LC circuit in series with the inductance of a 10-turn secondary winding that is resonant at the 60 Hz frequency of the AC voltage that is applied to the primary winding. What should be the value of C?

Expert Solution

Solution:

(a) Inductive reactance of solenoid = 927 ohm

resistance of solenoid winding = 0.254 ohm

(b) Impedance of solenoid winding = 927 ohm

(c) RMS magnetic flux = 0.00029 weber

(d) magnetic field along extended region = 0.148 Gauss

genius_generous answered 1 year ago

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