Question

6) Consider and RLC circuit with the three components making a loop. At time t=0 there...

6) Consider and RLC circuit with the three components making a loop. At time t=0 there is a charge Q0 on the capacitor and no current.

a) Write the equation for the voltage loop from Kirchoff’s law.

b) Use the relation between the current out of the capacitor and the change of its charge to express the answer to part a in terms of Q and its derivatives.

c) Guess a solution of the form Q(t)=Re{Aexp (-c t)} with Re the real part and A and C complex. What must A and c be?

d) Under what conditions will there be a solution with c positive and real?

e) What is the condition for the energy in the circuit to decay most rapidly?

f) For small R, what is the approximate oscillation frequency and time for the amplitude of Q to decay away?

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