rendered paste body<head><title>phys212/fall06 homeworkb 10</title></head><body><pre></pre> <h1>HomeworkB 10</h1> <h2>(6 questions)</h2><b>CLOSED -- changes no longer allowed. The deadline for storing your answers was 0800 on 11/07/2006.</b><br><b>The correct answers are marked "+". </b><b>The answers you chose are marked "X".</b><br><p>Consider the following circuit with a resistor and an inductor in series with an AC generator as shown below. The emf and frequency of the generator, as well as the values of the other components, are unknown (but greater than zero and finite).<P><img src=/cgi/courses/shell/common/showme.pl?courses/phys212/fall06/hwb/10/10/fig10.gif> <p><b>1)</b> For all values of ε<sub>m</sub>, ω, R, and L, the current through the resistor <blockquote><table><tr><td> </td><td> </td><td>leads the voltage across the generator</td></tr><tr><td><b>+</b> </td><td><font color=green><b>X</b></font> </td><td>lags the voltage across the generator</td></tr><tr><td> </td><td> </td><td>sometimes leads, sometimes lags the voltage across the generator (depending on ω, R, and L)</td></tr></table></blockquote><font color=green>The answer you chose (the one marked with an <b>X</b>) is the <b>correct answer</b>.</font><p> <p><b>2)</b> For all values of ε<sub>m</sub>, ω, R, and L, the peak voltage across the resistor is __________ the peak voltage from the generator.<blockquote><table><tr><td><b>+</b> </td><td><font color=green><b>X</b></font> </td><td>less than</td></tr><tr><td> </td><td> </td><td>greater than</td></tr><tr><td> </td><td> </td><td>sometimes less than, sometimes greater than (depending on ω, R, and L)</td></tr></table></blockquote><font color=green>The answer you chose (the one marked with an <b>X</b>) is the <b>correct answer</b>.</font><p><b>For the rest of the questions, assume the following values for the parameters: ε<sub>m</sub> = 38V, R = 10 Ω, and L = 4.7 mH (10<sup>-3</sup>H).</b> <p><b>3)</b> Assuming ω = 2π x 1220Hz, what is the peak voltage across the inductor?<blockquote><table><tr><td> </td><td> </td><td>12.3 V</td></tr><tr><td> </td><td> </td><td>27.8 V</td></tr><tr><td> </td><td> </td><td>29.8 V</td></tr><tr><td><b>+</b> </td><td><font color=green><b>X</b></font> </td><td>36.6 V</td></tr><tr><td> </td><td> </td><td>38 V</td></tr></table></blockquote><font color=green>The answer you chose (the one marked with an <b>X</b>) is the <b>correct answer</b>.</font><p> <p><b>4)</b> If we were to view the generator voltage as the input, and the voltage across the inductor as the output, this circuit behaves as a <blockquote><table><tr><td> </td><td> </td><td>low-pass filter</td></tr><tr><td><b>+</b> </td><td><font color=green><b>X</b></font> </td><td>high-pass filter</td></tr><tr><td> </td><td> </td><td>band-pass filter</td></tr></table></blockquote><font color=green>The answer you chose (the one marked with an <b>X</b>) is the <b>correct answer</b>.</font><p> <p><b>5)</b> For what frequency (in Hz) is the RMS output voltage (across the inductor) exactly half of the RMS input voltage (from the generator)?<blockquote><table><tr><td><b>+</b> </td><td><font color=green><b>X</b></font> </td><td>196 Hz</td></tr><tr><td> </td><td> </td><td>339 Hz</td></tr><tr><td> </td><td> </td><td>There is no frequency for which the RMS output voltage is exactly half of the RMS generator voltage.</td></tr></table></blockquote><font color=green>The answer you chose (the one marked with an <b>X</b>) is the <b>correct answer</b>.</font><p> <p><b>6)</b> If you were to add a 200 µF (10<sup>-6</sup>F) capacitor in series with the resistor and inductor in this circuit, and drive the circuit at ω = 2π x 1220Hz,<blockquote><table><tr><td><b>+</b> </td><td><font color=green><b>X</b></font> </td><td>the impedance of the circuit would decrease.</td></tr><tr><td> </td><td> </td><td>the impedance of the circuit would remain the same.</td></tr><tr><td> </td><td> </td><td>the impedance of the circuit would increase.</td></tr></table></blockquote><font color=green>The answer you chose (the one marked with an <b>X</b>) is the <b>correct answer</b>.</font><p><font size=1><address> © Copyright Department of Physics, University of Illinois at Urbana-Champaign. </address><font size=3></body></html>