# RLC Circuit (with critical and heavy damping)

1. Oct 15, 2011

### JNBirDy

1. The problem statement, all variables and given/known data
Consider a RLC circuit.

a) Suppose the parameters are chosen to give critical damping. The capacitor is charged to a voltage of V₀ and at time equal to zero the switch is closed. Find the time at which the magnitude of the current reaches a max, and find the value of the current at that time.

b) Consider the case of very heavy damping. Show that the charge on the capacitor declines approximately as e$^{-t/τ}$, where the τ (relaxation time) is approximately equal to RC.

2. Relevant equations
L(dI/dt) + RI + q/C = 0

τ= L/R

γ = R/L

Q = (1/R)√(L/C)

3. The attempt at a solution

Not sure how to start, any help is appreciated.

2. Oct 15, 2011

### SammyS

Staff Emeritus
Find out what critical & heavy damping are.