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Electronics: A Guide for Physicists (DRAFT -- in development)

Derek J. Thuecks

Section 3.10 Problems

  1. Calculate the energy (in Joules) stored in a \(2000\mu\text{F}\) capacitor charged to 5V.
  2. Calculate the impedance \(Z_{AB}\) and provide your answer in the form \(Z_{AB}=a+ib\) and \(Z_{AB}=\left|z\right|e^{i\theta}\) for each of the circuits in Figure 3.10.1-Figure 3.10.3.
    Figure 3.10.1.
    Figure 3.10.2.
    Figure 3.10.3.
  3. Design a low-pass RC filter that will attenuate a 60-Hz sinusoidal voltage by 12 dB relative to the dc gain. Use a \(100\Omega\) resistance. Explain in words why the low-pass RC filter attenuates the high frequencies.
  4. The circuit shown in Figure 3.10.4is used to trigger a device connected between terminals A and B. The device turns ON when \(V_{AB}\ge 6.0\text{V}\) and turns OFF when \(V_{AB}\le 2.0\text{V}\text{.}\) (Assume that connecting the device between terminals A and B has no effect o nthe rest of the circuit. In other words, the device effectively has almost infinite output resistance.)
    1. Assume that the switch has been in position Y for a long time. Then, at \(t=0\text{s}\text{,}\) the switch moves to position X. How long after the switch is turned to position X does the device turn ON?
    2. After being left at position X for over one minute, the switch is turned to position Y. How long does it take the device to turn off after this change?
    3. Use Python to plot your charging and discharging voltage curves (as a function of time).
    Figure 3.10.4.
  5. Use phasors to derive an expression for the voltage gain and phase shift for the following LR circuit.
    Figure 3.10.5.
  6. Sketch a graph of the magnitude of the impedance versus frequency for (a) a series RLC circuit and (b) a parallel RLC circuit. In each case, determine the phase of the impedance as the frequency passes through resonance.
  7. Use Python to plot the gain-versus-frequency curve and phase-versus-frequency curve for the circuit in Figure 3.10.6. I’d strongly recommend using Python to solve your system of equations.
    Figure 3.10.6.
  8. Use phasors to answer the following questions about the circuit in Figure 3.10.7.
    1. Show that the peak current through the resistor is
      \begin{equation*} I=\frac{V_0}{\sqrt{R^2 + \left(X_L^{-1}+X_C^{-1}\right)^{-2}}}\text{.} \end{equation*}
      (Hint: Find an equivalent impedance for the capacitor and inductor, and then examine the circuit behavior at a time when the resistor current \(I_R\) is purely real.)
    2. What is \(I_R\) in the limits \(\omega\rightarrow 0\) and \(\omega\rightarrow \infty\text{?}\)
    3. Find an expression for the resonance frequency \(\omega_0\text{?}\) What is \(I_R\) at this frequency?
      Figure 3.10.7.
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