Problem 30.60 A charged capacitor with C = 750 ? F is connected in series to an

Question

Problem 30.60

A charged capacitor with C = 750?F is connected in series to an inductor that has L = 0.290H and negligible resistance. At an instant when the current in the inductor is i = 2.40A , the current is increasing at a rate of di/dt=89.0A/s.

Part A

During the current oscillations, what is the maximum voltage across the capacitor?

Express your answer to three significant figures and include the appropriate units.

Problem 30.60

A charged capacitor with C = 750?F is connected in series to an inductor that has L = 0.290H and negligible resistance. At an instant when the current in the inductor is i = 2.40A , the current is increasing at a rate of di/dt=89.0A/s.

Part A

During the current oscillations, what is the maximum voltage across the capacitor?

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

let Vo is the initial voltage across capacitor.

First Apply, Energy conservation

0.5*C*vo^2 = 0.5*L*I^2

==> Vo = I*sqrt(L/C)

= 2.4*sqrt(0.29/(750*10^-6))

= 47.2 volts

now Petentail diffrence across inductor, vL = L*dIdt

= 0.29*89

= 25.81 volts

we know, Vo = vL + vC

==> vC = Vo - vL

= 47.2 - 25.81

= 21.39 volts <<<<<<<<----------Answer

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