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

Here ,

for di/dt = 89 A/s

Vc = Ldi/dt

Vc = 0.290 * 89

Vc = 25.81 V

Now ,for Vmax

0.5 C Vmax^2 = 0.5 * c*Vc^2 +0.5 Li^2

0.5 * 750 * 10^-6 * Vmax^2 = 0.5 * 750 *10^-6 * 25.81^2 + 0.5 * 0.29 * 2.4^2

solving for Vmax

Vmax = 53.8 V

the maximum capacitor volatge is 53.8 V

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