A resistor ($R$) and an inductor ($L$) are in parallel. What is the effective impedance, $Z_{eff}$ across these elements? 1. $R + L$ 2. $R + i\omega L$ 3. $1/(R+i\omega L)$ 4. $\dfrac{1}{1/R -i/(\omega L)}$ 5. Something else? 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
AC voltage $V$ and current $I$ vs time $t$ are as shown: <img src="./images/IV_graphs.png" align="center" style="width: 600px";/> The graph shows that.. 1. $I$ leads $V$ ( $I$ peaks before $V$ peaks ) 2. $I$ lags $V$ ( $I$ peaks after $V$ peaks ) 3. Neither Note: * Correct Answer: B
Suppose you have a circuit driven by a voltage: $$V(t)=V_0\cos(\omega t)$$ You observe the resulting current is: $$I(t) = I_0\cos(\omega t-\pi/4)$$ Would you say the current is 1. leading 2. lagging the voltage by 45 degrees? Note: * Correct Answer: B
Consider an RC circuit attached to a sinusoidally driven voltage source. If at $t=0$ we turn on the source, $I(t=0)=\frac{V_0}{R}$. Then the current follows this solution, $$I(t) = \dfrac{V_0}{\sqrt{R^2+\frac{1}{\omega^2C^2}}}\cos(\omega t + \phi) - \left(\dfrac{V_0}{R}-\dfrac{V_0\cos\phi}{\sqrt{R^2+\frac{1}{\omega^2C^2}}}\right)e^{-t/RC}$$ What happens to the long term current as $\omega \rightarrow 0$? 1. goes to zero 2. goes to $\dfrac{V_0}{R}$ 3. goes to infinity 4. Something else Note: * Correct answer: A
Consider an RC circuit attached to a sinusoidally driven voltage source. If at $t=0$ we turn on the source, $I(t=0)=\frac{V_0}{R}$. Then the current follows this solution, $$I(t) = \dfrac{V_0}{\sqrt{R^2+\frac{1}{\omega^2C^2}}}\cos(\omega t + \phi) - \left(\dfrac{V_0}{R}-\dfrac{V_0\cos\phi}{\sqrt{R^2+\frac{1}{\omega^2C^2}}}\right)e^{-t/RC}$$ What happens to the long term current as $\omega \rightarrow \infty$? 1. goes to zero 2. goes to $\dfrac{V_0}{R}$ 3. goes to infinity 4. Something else Note: * Correct answer: B