A 1.5 mu F capacitor is charged to 60 V. The charging battery is then disconnect
ID: 1555952 • Letter: A
Question
A 1.5 mu F capacitor is charged to 60 V. The charging battery is then disconnected and a 25 mH coil is connected in series with the capacitor. a. What is the maximum current in the coil? b. When the capacitor has a potential difference of 20 V, what is the emf across the coil? c. When the capacitor has a potential difference of 20 V, what is the energy stored in the magnetic field? d. When the capacitor has a potential difference of 20 V, what is the current in the circuit? e. What is the frequency of the oscillation in the circuit?Explanation / Answer
(a)
angular frequency w = 1/sqrt(LC) = 5164 /s
Imax = w*C*E = C*E/sqrt(LC)
Imax = 1.5*10^-6*60/sqrt(25*10^-3*1.5*10^-6)
Imax = 0.465 A
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(b)
VC + VL = 60
VL = 40 V
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(c)
total energy Utot = (1/2)*C*E^2 = (1/2)*1.5*10^-6*60^2 = 0.0027
when potential across capacitor = 20
Uc = (1/2)*C*v^2 = (1/2)*1.5*10^-6*20^2 = 0.0003 J
energy stored in magnetic field
UL = Utot - Uc = 0.0024 J
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(d)
vc = E*coswt
20 = 60*cos(5164*t)
t = 6.6*10^-5 s
i = Imax*sinwt
i = 0.465*sin(5164*6.6*10^-5)
i = 0.155 A
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(e)
f = w/2pi
f = 5164/(2*pi) = 822 Hz
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