Problem

An $R L C$ circuit with $R=20.0 \Omega, L=295 \ma…

07:06

Problem 86 Hard Difficulty

You are given a sealed box with two electrical terminals. The box contains a $5.00-\Omega$
resistor in series with either an inductor or a capacitor. When you
attach an ac generator with an rms voltage of 0.750 $\mathrm{V}$ to the terminals of the box, you find that the current increases with increasing frequency. (a) Does the box contain an inductor or a capacitor? Explain. (b) When the frequency of the generator is 25.0 $\mathrm{kHz}$ , the
rms current is 87.2 $\mathrm{mA}$ . What is the capacitance or inductance of
the unknown component in the box?

Answer

a) see explanation
b) see work

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Physics 102 Electricity and Magnetism

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Watch More Solved Questions in Chapter 24

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Video Transcript

the first item. We have to remember the following voltage. The ROMs Voltage is a question that Ari Mass current times impedance then the current. Is it close to the voltage divided by Olympians? As we increase the frequency, we get an increase in the current if the current is increasing and we're not changing the search so the voltage is held. The same means that impedance is decreasing. Now remember that the people's he's given by discredit off our square plus XY squared. If we have a capacitor connected toe or wherever it sister or Izzy is, he goes to the square it off R Squared plus Excel squared. If we have a new doctor instead, no, we have to decide. How can you decide using these information? So by increasing the frequency, we are decreasing impedance. Then what happens? Toa Each of the react Ince's when we increase the frequency, remember that the capacitive inductive reactors is equals to two pi times the frequency times getting doctors. By increasing the frequency, we end up increasing the reactors, which increases they see this which will instead decrease the current show. What is connected to our resistance is a capacitor and we can check for consistence. The reactor's they're active capacitance is it cost you one divided by their frequency times the capacitance. Look that Oh, Megan is It goes to two pi times f and usually one refers to both omega and F as the frequency. Then, by increasing the frequency, we are decreasing the reactive capacitance which decreases impedance has wanted. So we have. He could pass it or connected toe a resistor. On the second item, we are told that when the frequency is a close to 25 kilo hertz, the current the R. M s current is equal to wait 7.2 merely appears. And now we have to discover what is the capacitance over capacity. As we already know that there is a capacitor connected to the resistance. In order to do that, we have to use this information So they are a mask. Current is equals to devote edge divided by the impedance. Then using the values given by the problem, we get 87 points true time. Stand to the ministry. Easy clothes too. The voltage, which is 0.75 divided by the impedance, the beauteous the square. It off, the resistance is squared. So 25 it was the capacity reactors squared. No, we can calculate the capacity reactant by solving this equation for XY. We're doing this by changing this terms. To get square it off. 25 plus XY squared is a course to 0.75 divided by 87.2 times 10 to the minus street. Then we square both sides to get 25. It was X c squared easy course. True 0.75 divided by 87.2 times 10 to the ministry. Finally XY squared is equals two plus or minus The square root 0.75 divided by 87 points True times 10 to the minus Tree miners 25 noted that I forgot an important thing here. From the step to the step, I squared both sides so I forgot one square. Here then you're fine square here. That's it. No, our capacity react ins is approximately six 0.998 homes. It was, But this is not everything. Well, we have a pleasure Minors. Here we choose the plus. I know because there are no negative react Ince's then we now have to complete the capacitance. Remember that the reactor's Izzy Costa one divided by true pi times the frequency times like a past tense, then capacitance. He's equals to one divided by two pi times the frequency times the reactors, putting the values given in the problem. We have two pi times, 25 time. Stand to the third because there is a kilo here times 6.998 under one. Finally, our capacitance is approximately zero 0.91 Negro for its

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