Homework Assignment 9 (due Sunday 4/12)

PHYS112 : Homework Assignments

AC Circuits

Goals :

Apply the generalized Ohm's Law to series LRC circuits driven by AC signals

$\begin{displaymath} i = \frac{\mathcal{E}}{Z} \hspace{2cm} Z = \sqrt{R^2 + (X_L - X_C)^2} \end{displaymath}$

where and $\mathcal{E}$ are amplitudes, and the capacitive and inductive reactances are given by

$\begin{displaymath} X_C = \frac{1}{\omega^\mathrm{dr} C} \hspace{2cm} X_L = \omega^\mathrm{dr} L \end{displaymath}$
Interpret the associated phasor diagrams

$\begin{displaymath} \mathcal{E} = \sqrt{\Delta V_R^2 + (\Delta V_L - \Delta V_C)^2} \hspace{2cm} \tan \phi = \frac{X_L - X_C}{R} \end{displaymath}$
Understand the concept of resonance in series LRC circuits

$\begin{displaymath} X_L=X_C \hspace{1cm} \phi=0 \hspace{1cm} \omega = \frac{1}{\sqrt{LC}} \end{displaymath}$
Calculate the average power dissipated in an LRC circuit

$\begin{displaymath} \left<P\right> = \mathcal{E}^\mathrm{rms} I^\mathrm{rms} \cos \phi = (I^\mathrm{rms})^2 R \end{displaymath}$

$\begin{displaymath} \mathcal{E}^\mathrm{rms} = \frac{\mathcal{E}^\mathrm{max}}{\sqrt{2}}, I^\mathrm{rms} = \frac{I}{\sqrt{2}} \end{displaymath}$

Your assignment is posted on the UT Homework Service (Class no. 99940)