A series circuit has a sinusoidal voltage supplied to it at $632 \mathrm { kHz }$ with a peak voltage of $748 \mathrm {~V}$ It also contains a $\text { 25-k } \Omega$ resistance, a $16 - \mu \mathrm { F }$ capacitance, and a $30 - H$ inductance. What is the peak current for this circuit?

Question

Quizplus · Accepted Answer

First, we need to calculate the impedance of the circuit:
\begin{align*}
Z = \sqrt{R^2+\left(X_L-X_Cight)^2} &= \sqrt{\left(25,000~\Omegaight)^2 + \left[\left(2\pi f Light) - \frac{1}{2 \pi f C}ight]^2} \
&= \sqrt{\left(25,000~\Omegaight)^2 + \left[\left(2\pi \cdot 632 \cdot 10^3~\mathrm{Hz} \cdot 30~\mathrm{H}ight) - \frac{1}{2 \pi \cdot 632 \cdot 10^3~\mathrm{Hz} \cdot 16 \cdot 10^{-6}~\mathrm{F}}ight]^2} \
&= 10,206~\Omega
\end{align*}

Next, we can use Ohm's law to find the peak current:
\begin{align*}
I_{\mathrm{peak}} &= \frac{V_{\mathrm{peak}}}{Z} \
&= \frac{748~\mathrm{V}}{10,206~\Omega} \
&\approx 0.073~\mathrm{A} \
&= 73~\mathrm{mA} \
&= 7.3 	imes 10^{-5}~\mathrm{A} \
&= \boxed{6.3~\mu\mathrm{A}} 	ext{ (rounded to 2 significant figures)}
\end{align*}

A Series Circuit Has a Sinusoidal Voltage Supplied to It 632kHz632 \mathrm { kHz }632kHz

A Series Circuit Has a Sinusoidal Voltage Supplied to It $632 \mathrm { kHz }$