A long solenoid with circular cross section of radius r 1 = 2.80 cm and n = 287

Question

A long solenoid with circular cross section of radius r1 = 2.80 cm and n = 287 turns/cm is inside and coaxial with a short coil with circular cross section of radius r2 = 4.70 cm and N = 31 turns (see figure below). Treat the solenoid and coil as a transformer.

    (a) Find the root-mean-square voltage in the coil if the solenoid has a root-mean-square voltage of 120 V and a frequency of 60 Hz. The length of the solenoid is 19.0 cm.
         
    
    (b) What is the voltage in the coil if the frequency is 0 Hz (DC current)?
    

A long solenoid with circular cross section of radius r1 = 2.80 cm and n = 287 turns/cm is inside and coaxial with a short coil with circular cross section of radius r2 = 4.70 cm and N = 31 turns (see figure below). Treat the solenoid and coil as a transformer.

Explanation / Answer

a)

Nc =31

Ns =nL=287*19 =5453 turns

Vc/Nc =Vs/Ns

Vc =Vs*(Nc/Ns)

Vc =120*(31/5453)

Vc=0.682 V

b)

With DC current ther is no change in magnetic flux,in solenoid ,so there is no voltage in coil.

V=0 V

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