Find the period of the oscillation from the formula for angular frequency in terms of L and C. The time required is one-fourth of the period.
a) After the switch is thrown to position b the circuit is an LC circuit.
b) What is the starting charge on the capacitor when the switch is thrown from position a to position b? Use energy conservation to find the maximum current.
a) Consider the total energy and apportion between electric and magnetic contributions as indicated in the problem statement.
b) Solve the equation relating q(t) and qmax at time t=0 and use the charge ratio found above in part a.
a) Use the formula for the natural frequency of the circuit; evaluate the square root of the ratio of the capacitances.
b) Evaluate the parallel capacitance added to each quantity under the square root sign to get a ratio of frequencies of 2.96.
a) Find the energy at the time that the charge and current have the stated values. This will be the total energy of the system, constant since there is no loss (no R) in the circuit.
b) Assume that all the energy is stored in the capacitor. To what charge does that correspond?
b) Assume that all the energy is stored in the inductor. To what current does that correspond?
d,e) Solve the equation relating q(t) and qmax at time t=0 and use the two values of charge above.