What is $(1+i)^2/(1-i)$? 1. $e^{i\pi/4}$ 2. $\sqrt{2}e^{i\pi/4}$ 3. $e^{i3\pi/4}$ 4. $\sqrt{2}e^{i3\pi/4}$ 5. Something else! Note: *Correct Answer: D

## Announcements * Project problems are graded * Sync your repositories to receive feedback * Responding to your feedback is a big part of the next project problem * Quiz 3 (next Friday 2/17) - RLC circuits * Solve a circuit problem using the phasor method * Discuss limits on the response and how it might act as a filter

For the RL circuit with driving voltage of $V(t) = V_0 \cos (\omega t)$, we found a solution for the current as a function of time, with $I=0$ at $t=0$, $$I(t) = a \cos(\omega t + \phi) - a\cos(\phi) e^{-Rt/L}$$ where $a = \frac{V_0}{\sqrt{R^2+L^2\omega^2}}$ and $\phi = \tan^{-1}(-L\omega/R)$. What happens to the current when $\omega \rightarrow \infty$? 1. Current is essentially zero, for all time 2. Current dies off completely, eventually goes to zero 3. Eventually, current is constant, $V_0/R$ 4. It depends 5. ???

For the RL circuit with driving voltage of $V(t) = V_0 \cos (\omega t)$, we found a solution for the current as a function of time, with $I=0$ at $t=0$, $$I(t) = a \cos(\omega t + \phi) - a\cos(\phi) e^{-Rt/L}$$ where $a = \frac{V_0}{\sqrt{R^2+L^2\omega^2}}$ and $\phi = \tan^{-1}(-L\omega/R)$. What happens to the current when $\omega \rightarrow \infty$? 1. Current is essentially zero, for all time 2. Current dies off completely, eventually goes to zero 3. Eventually, current is constant, $V_0/R$ 4. It depends 5. ???

Which point below best represents $4e^{i3\pi/4}$ on the complex plane? <img src="./images/complex_numbers_graph.png" align="center" style="width: 600px";/> Note: * Correct Answer: D

<img src="./images/RLC.png" align="right" style="width: 400px";/> What is the total impedance of this circuit, $Z_{total}$? 1. $R + i\left(\omega L + \frac{1}{\omega C}\right)$ 2. $R + i\left(\omega L - \frac{1}{\omega C}\right)$ 3. $\frac{1}{R} + \frac{1}{i\omega L} + {i \omega C}$ 4. $\dfrac{1}{\frac{1}{R} + \frac{1}{i\omega L} + {i \omega C}}$ 5. None of these Note: * Correct Answer: B