Question

An LC circuit like the one in the figure below contains an 65.0 mH inductor and a 10.0 pF capacitor that initially carries a 175 UC charge. The switch is open for t < 0 and is then thrown closed at t = 0. lle (a) Find the frequency (in hertz) of the resulting oscillations. 197 HZ (b) At t = 1.00 ms, find the charge on the capacitor. 174 x Remember that your answer to part (a) is in hertz rather than radians/ second. PC (c) At t = 1.00 ms, find the current in the circuit. | mA (d) What If? What are the first three times (in ms), after t = 0, when the capacitor is fully charged again? smallest value ms ms largest value

Answer 1

▪︎Givens:

  L = 65 mH = 65 × 10^-3 H

C = 10 = 10 × 10^-6 F

µF

q = 175 $\mu C$ = 175 × 10^-6 C

a) $f=\frac{1}{2\pi\sqrt{LC}}$

  $f=\frac{1}{2\pi\sqrt{(65\times10^-^3)\times(10\times10^-^6)}}$

= 197.4 Hz

b) $\omega =2\pi f$

$=2\pi \times197.4$

= 1240.3 rad/s

  $q=A\,cos\,\omega t$

  $=(175\times10^-^6)\,cos\,(1240.3\times1\times10^-^3)$

= 1.75 × 10^-4 C

= 175 $\mu C$

c) Current, $I=\frac{dq}{dt}=-A\omega\,\,sin\,\,\omega t$

$=-175\times10^-^6\times1240.3\,\,sin\,\,(1240.3\times1\times10^-^3)$

= 4.7 × 10^-3 A

= 4.7 mA