In an oscillating LC circuit, L = 4.24 mH and C = 3.02 μF. At t = 0 the charge on the capacitor is zero and the current is 2.38 A. (a) What is the maximum charge that will appear on the capacitor? (b) At what earliest time t > 0 is the rate at which energy is stored in the capacitor greatest, and (c) what is that greatest rate?

a) 2.693*10^-4 C

b) 8.875*10^-5 s

c) 2.96 W

Explanation:

Given that

Inductance of the circuit, L = 4.24 mH

Capacitance of the circuit, C = 3.02 μF

Current in the circuit, I = 2.38 A

See attachment for calculations

a) 0.269 mC

b) 0.355 ms

c) 1.39W

Explanation:

a) To find the charge off the capacitor you start by using the following expression for the charge in the capacitor:

next, you calculate the current I by using the derivative of q:

( 1 )

L: inductance = 4.24*10^{-3}H

C: capacitance = 3.02*10^{-6}F

I: current = 2.38 A

you replace the values of the parameters in (1):

b) to find the time t you use the following formula for the energy of the capacitor:

the maximum storage energy in the capacitor is obtained by derivating the energy:

hence, the time is 0.355 ms

c) The greatest rate is obtained for duc/dt evaluated in t=0.355 ms: