You have a parallel-plate ideal capacitor with a capacitance of 24 ?F that you c

Question

You have a parallel-plate ideal capacitor with a capacitance of 24 ?F that you connect to a 3 V battery until it is fully charged.  Then, you disconnect the capacitor from the battery, and put this charged capacitor in series with an ideal 100 mH solenoid inductor.  The solenoid is 6 cm long, has 124 turns, and is filled with air.  You complete the final connection to the inductor at t=0.

      (a)  What is the diameter of the solenoid?

      (b)  The capacitor starts with its maximum charge, and starts discharging through the inductor. What is this maximum charge on the capacitor?  

      (c)  What is the energy stored in the capacitor at this time?

      (d)  What is the first time after t=0 that the current has its maximum value?

      (e)  Consider a time when the charge on the capacitor is equal to 0.5 times the maximum value found in part (b).  What is the current through the inductor at this time? (Note: the fastest way to solve this uses energy concepts.)

Explanation / Answer

a) L(inuctance) = mue*N^2*A/L

100*10^-3 = 4*3.14*10^-7*124^2*(3.14*r^2)/0.06


r = sqrt(0.1*0.06/(4*3.14^2*124^2*10^-7))

= 0.3145 m

d = 2*r = 0.629 m

b)

Qo = C*vo = 24*10^-6*3 = 72*10^-6 C

c) U = 0.5*Qo*Vo = 108*10^-6 J = 1.08*10^-4 J

d) initially inductor acts as open circuit.

so. i = 0

e)

b) when U = 0.5*Q*vo

= 0.5*0.5*Qo*Vo

= Umax/2


UB = 0.5*L*i^2

Umax/2 = 0.5*L*i^2

i = sqrt(Umax/(4*L))
= sqrt(1.08*10^-4/(4*0.1))
= 1.643*10^-2 A

= 16.43 mA

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