Write an equation that solves for the admittance (Y) of this parallel circuit. (d) Write an equation for the voltage drop across the resistor as a function of time when \(\displaystyle ω=ω_R\). For successful circuit-building exercises, follow these steps: For AC circuits where inductive and capacitive reactances (impedances) are a significant element in the calculations, I recommend high quality (high-Q) inductors and capacitors, and powering your circuit with low frequency voltage (power-line frequency works well) to minimize parasitic effects. Its purpose is to get students thinking in terms of parallel admittances, in a manner similar to parallel conductances. Calculate the total impedance offered by these three capacitors to a sinusoidal signal with a frequency of 4 kHz: This question is another example of how multiple means of calculation will give you the same answer (if done correctly!). Write the equation for the voltage across it if the inductance is 40 mH. Like conductance, both these reciprocal quantities are measured in units of siemens. An ac generator is connected to a device whose internal circuits are not known. However, students will have a much better understanding of phasors and complex numbers in AC circuits if you hold them accountable to representing quantities in that form. This is another reason why capacitors are generally favored over inductors in applications where either will suffice. L = 40 × 10-3 H; i = 0.1 sin (200t – 40º). Write down the equation for a sinusoidal voltage of 50 Hz and its peak value is 20 V. Draw the corresponding voltage versus time graph. What is the power dissipated in the resistor? What. 5. = .612 Ohms), then find C. 0000003650 00000 n Calculate the average power output of the source if it is connected across, 31. Furthermore, having students build their own practice problems teaches them how to perform primary research, thus empowering them to continue their electrical/electronics education autonomously. Identify another possible failure in this circuit which would result in no doorbell action (no sound) and no light at the lamp. Discuss problem-solving strategies in class so that students understand how and why it is possible to determine Θ. Secondly, this is an interesting question because it shows how something as abstract as phase angle can be measured with just a voltmeter - no oscilloscope required! 7. Voltage divider circuits may be constructed from reactive components just as easily as they may be constructed from resistors. (b) What is unreasonable about this result? (b) Write an expression for the current through the inductor. 3. Does this mean that the electric motor, which is electrically equivalent to the LR network, will dissipate the same amount of heat? [I1’ = current through the capacitor due to 50 ∠ 0o V source]. your students are thinking. Another reason for following this method of practice is to teach students scientific method: the process of testing a hypothesis (in this case, mathematical predictions) by performing a real experiment. (b) If the frequency is changed to 60 Hz while keeping the voltage amplitude at 160 V, what are the capacitive reactance and the current amplitude? The source for the circuit has an rms emf of 240 V at a frequency of 60 Hz. It has been my experience that students require much practice with circuit analysis to become proficient. Use the simplified circuit shown below. This dissipative behavior is typically modeled as a series-connected resistance: Calculate the magnitude and phase shift of the current through this capacitor, taking into consideration its equivalent series resistance (ESR): Compare this against the magnitude and phase shift of the current for an ideal 0.22 μF capacitor. If your goal is to educate theoretical physicists, then stick with abstract analysis, by all means! 0000004526 00000 n 8. A 1132.1 Ω resistor connected in series with a 269.6 nF capacitor would suffice. 24. 16. Why it is 0 degrees, and not some other angle? 50. One way to vary the amount of power delivered to a resistive AC load is by varying another resistance connected in series: A problem with this power control strategy is that power is wasted in the series resistance (I2Rseries). The equation need not solve for the phase angle between voltage and current, but merely provide a scalar figure for admittance (in siemens): Follow-up question #1: draw a phasor diagram showing how Y, G, and B relate. (b) Show that for high frequencies, \(\displaystyle v_{out}≈v_{in},\) but for low frequencies, \(\displaystyle v_{out}≈0\). (a) What is rms current in the transmission line? (b) Write an expression for the current output of the source. a.) Asking students to determine how they would connect an oscilloscope to the circuit to measure Θ is an exercise in developing their abstraction abilities between calculations and actual circuit scenarios. A 500 μH inductor, 80/π2 pF capacitor and a 628 Ω resistor are connected to form a series RLC circuit. 13. Note also how the inductor and capacitor drop very disparate amounts of voltage at the high and low frequencies. 0000002394 00000 n A teaching technique I have found very helpful is to have students come up to the board (alone or in teams) in front of class to write their problem-solving strategies for all the others to see. The given equation is υ = 10sin (3 π×104 t). requires the fewest steps)? The current in an inductive circuit is given by 0.3 sin (200t – 40°) A. A 25-μF capacitor is connected to an emf given by \(\displaystyle v(t)=(160V)sin(120πt)\). Explain how this system works, in your own words. (d) Write voltage drops across the resistor, capacitor, and inductor and the source voltage as a function of time. A coil with a self-inductance of 16 mH and a resistance of 6.0Ω is connected to an ac source whose frequency can be varied. �U c������~���#�������0���. A 20-Ω resistor, 50-μF capacitor, and 30-mH inductor are connected in series with an ac source of amplitude 10 V and frequency 125 Hz. Consider the LC circuit to the right. Show that the SI unit for capacitive reactance is the ohm. Thus, the current through 5Ω resistor, using the principle of superposition is. 23. MFMcGraw-PHY 2426 Chap31-AC Circuits-Revised: 6/24/2012 3 Generators By turning the coils in the magnetic field an emf is generated in the coils thus turning mechanical energy into alternating (AC) power. The input voltage to the circuits is \(\displaystyle v_{in}\), and the output voltage is \(\displaystyle v_{out}\). As usual, the real point of this question is to get students to think about the analytical procedure(s) they use, and to engage their minds in problem-solving behavior. 0000003428 00000 n Specifically, will increasing the resistance make the phase shift approach -90o or approach 0o? Calculate the total impedance offered by these two capacitors to a sinusoidal signal with a frequency of 900 Hz: Ztotal = 411.3 Ω ∠−90o or Ztotal = 0 − j411.3 Ω.

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