Question

A charged capacitor is connected to an ideal inductor. At time t = 0, the charge on the capacitor is equal to 6.00 μC. At time t = 2.00 ms the charge on the capacitor is zero for the first time. What is the amplitude of the current at that same instant?

Answer 1

Answer:

$4.71\times 10^{-3}A$

Explanation:

$Q_{max}$ = Maximum charge stored by capacitor = 6 μC = 6 x 10⁻⁶ C

$t$  = time taken for charge on the capacitor to become zero = 2 ms = 2 x 10⁻³ s

Time period is given as

$T = 4t$

$T = 4(2\times 10^{-3})$

$T = 8\times 10^{-3} s$

Angular frequency is given as

$w = \frac{2\pi }{T}$

$w = \frac{2(3.14) }{8\times 10^{-3}}$

$w$ =785 rad/s

Charge at any time is given as

$Q(t) = Q_{max}Coswt$

Taking derivative both side relative to "t"

$\frac{\mathrm{d}Q(t) }{\mathrm{d} t} = \frac{\mathrm{d}(Q_{max}Coswt) }{\mathrm{d} t}$

$i(t)= -Q_{max} w Sinwt$

Amplitude of the current is given as

$i_{max}= Q_{max} w$

$i_{max}= (6\times 10^{-6}) (785)$

$i_{max}= 4.71\times 10^{-3}A$