Question

An LC circuit consists of a 3.4-µF capacitor and a coil with a self-inductance 0.080 H and no appreciable resistance. At t = 0 the capacitor has a charge of 5.4 µC and the current in the inductor is zero. (a) How long after t = 0 will the current in the circuit be maximum? (b) What will be this maximum current?

Answer 1

Answer

given,

capacitance = C = 3.4-µF

inductance = L = 0.08 H

frequency is expressed as

$f = \dfrac{1}{2\pi\sqrt{LC}}$

time period

$T = \dfrac{1}{f}=2\pi\sqrt{LC}$

after time T/4 current reach maximum

 $t = \dfrac{T}{4}$

 $t = \dfrac{2\pi\sqrt{LC}}{4}$

 $t = \dfrac{2\pi\sqrt{0.08 \times 3.4 \times 10^{-6}}}{4}$

        t = 8.2 x 10⁻⁴ s

        t = 0.82 ms

b) using law of conservation

  $\dfrac{1}{2}CV^2=\dfrac{1}{2}LI^2$

  $I^2 = \dfrac{CV^2}{L}$

  $I^2 = \dfrac{C}{L}\dfrac{Q^2}{C^2}$

  $I =\sqrt{\dfrac{Q^2}{CL}}$

  $I =\sqrt{\dfrac{(5.4 \times 10^{-6})^2}{0.08 \times 3.4 \times 10^{-6}}}$

       I = 0.010 A

       I = 10 mA