Question 89: AC fundamentals

Question

An oscillating LC circuit consists of a $$75 ~\mathrm{mH}$$ inductor and a $$1.2 ~\mu \mathrm{F}$$ capacitor. If the maximum charge to the capacitor is $$2.7 ~\mu \mathrm{C}$$. The maximum current in the circuit will be ___________ $$\mathrm{mA}$$

Accepted Answer

The maximum current in an LC circuit can be found using the following formula related to simple harmonic motion:
$I_{	ext{max}} = \omega Q_{	ext{max}}$,
where:
$I_{	ext{max}}$ is the maximum current,
$\omega$ is the angular frequency, and
$Q_{	ext{max}}$ is the maximum charge on the capacitor.
The angular frequency $\omega$ for an LC circuit is given by:
$\omega = \frac{1}{\sqrt{LC}}$,
where:
$L$ is the inductance, and
$C$ is the capacitance.
Given that $L = 75 \, 	ext{mH} = 75 	imes 10^{-3} \, 	ext{H}$, $C = 1.2 \, \mu 	ext{F} = 1.2 	imes 10^{-6} \, 	ext{F}$,
and $Q_{	ext{max}} = 2.7 \, \mu 	ext{C} = 2.7 	imes 10^{-6} \, 	ext{C}$,
we can substitute these values into the formulas to find $I_{	ext{max}}$:
$\omega = \frac{1}{\sqrt{(75 	imes 10^{-3})(1.2 	imes 10^{-6})}} = 3333.33 \, 	ext{rad/s}$,
$I_{	ext{max}} = \omega Q_{	ext{max}} = 3333.33 	imes 2.7 	imes 10^{-6} = 0.009 \, 	ext{A}$.
Therefore, the maximum current in the circuit is $0.009 \, 	ext{A}$, or equivalently, $9 \, 	ext{mA}$.

AC fundamentals

An oscillating LC circuit consists of a $75 ~\mathrm{mH} inductor and a 1.2 ~\mu \mathrm{F} capacitor. If the maximum charge to the capacitor is 2.7 ~\mu \mathrm{C}. The maximum current in the circuit will be ___________ \mathrm{mA}

Choose the correct answer: