A 1.5 mu F capacitor is charged to 60 V. The charging battery is then disconnect

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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