A 18.0F capacitor is placed across a 22.5V battery for a few seconds and is then

Question

A 18.0F capacitor is placed across a 22.5V battery for a few seconds and is then connected across a 12.0mH inductor that has no appreciable resistance.

Part A

After connecting the capacitor and inductor together, find the maximum current in the circuit.

Part B

When the current is a maximum, what is the charge on the capacitor?

Part C

How long after connecting the capacitor and inductor together does it take for the capacitor to be completely discharged for the first time?

Part D

How long after connecting the capacitor and inductor together does it take for the capacitor to be completely discharged for the second time?

Explanation / Answer

(a)
Using Energy Conservation,

1/2 * C*v^2 = 1/2 * L*imax^2
1/2 * 18.0 * 10^-6 * 22.5^2 = 1/2*12.0 * 10^-3 * imax^2
imax =  0.87 A

(b)
When the energy has been completely transferred to the inductor, the energy stored in the capacitor is zero, so its charge will then be zero.

(c)
t = 2**sqrt(LC)
t = 2**sqrt(12.0*10^-3 * 18.0*10^-6)
t = 2.9 ms

V = 22.5 cos(wt)
The capacitor will be completely discharged for the first time, when V = 0 - i.e. after a time equal to 1/4 period = 730us, and for the second time half a period later again - i.e. after total (3/4 period) = 2.17ms

t1 = 730 us

(d)
t2 = 2.17 ms

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.