Question

Calculate Maximum current in the circuit , if capacitor of capacitance 1μF is charged to a potential of 2V and is connected in parallel to an inductor of inductance 10⁻³ H?
(Please give answer in mA of current)

Answer 1

When a capacitor is connected to an inductor with the initial conditions as:
The capacitor is charged to potential V₀ and there is no current flowing in the circuit, the current builds up in the circuit as formula given by

$I(t)= I_0\ sin(wt)\\where\ I_0=maximum\ current\ in\ circuit=\frac{V_0}{ \sqrt{ \frac{L}{C} } }$

given that C = 1μF, V₀ = 2V, L = 10⁻³ H

$I_0=\frac{V_0}{ \sqrt{ \frac{L}{C} } }=\frac{2}{ \sqrt{ \frac{10^{-3}}{10^{-6}} } }A= \frac{2}{ \sqrt{1000} }\ A\\ \\converting\ to\ mA\\ \\I_0=\frac{2}{ \sqrt{1000} }\ A=\frac{2}{ \sqrt{1000} }*1000\ mA\\ \\I_0= \frac{ \sqrt{4*10^6} }{ \sqrt{1000} }\ mA =\boxed{ \sqrt{4000}\ mA}$