- #1

ayoubster

- 8

- 0

## Homework Statement

A certain circuit has a resistance of 30 Ω, inductance of 5.0 mH, and capacitance of 0.375 µF. At time t=0, the capacitor is charged with 4.0 µC on the top plate (and -4.0 µC on the bottom), and the switch is then thrown so that the capacitor can discharge through the inductor and resistor.

(a) What is the frequency at which this circuit will oscillate?

(b) How long will it take the circuit to decay to an amplitude of 1% the initial amplitude?

(c) Suppose we took out the capacitor, and instead allowed a current to decay through the resistor and inductor. How long would it take to reach 1% of the initial current?

## Homework Equations

ω = √((1/LC) - (R/2L)^2)

ω = 1/√LC

q = q

_{o}e

^{-t/τ}

V = V

_{o}e

^{-t/τ}

where τ = RC

## The Attempt at a Solution

Plugging in my values for a) gives me 22.9kHz, which seems reasonable, however I'm not sure if I should be using the first frequency equation or the second.

Moreover, I have no idea what to do for (b) and (c). I tried using the 3rd equation, where 1% of the charge would be .04μC, taking the ln of both sides would let me solve for t, however I'm really not sure about this..

I'm completely lost on (c), as I thought if they asked for current, I can solve for my voltage and my current using my values, however doesn't Q = CV only work for RC circuits?