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The "square-wave" voltage shown in FIGURE $24-31$ is applied to an $R C$ circuit. Sketch the shape of the instantaneous voltage across the capacitor, assuming the time constantof the circuit is equal to the period of the applied voltage.

$\therefore$ Voltage across capacitor for decreases form 0.588 $\mathrm{V}$ to 0.3566 $\mathrm{V}$ during the period $2.5 \mathrm{T}<\mathrm{t}<3 \mathrm{T}$

Physics 102 Electricity and Magnetism

Chapter 24

Alternating-Current Circuits

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Alternating Current

Cornell University

Rutgers, The State University of New Jersey

Hope College

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for this problem were given a graph that shows the voltage Nick capacitor over time one is connected to a battery were also given the resistance, which is our is equal to 4000 700 Holmes, part A for us to find the voltage in this battery. Well, once the capacity reaches maximum charge, it will be the same voltage as the battery so it levels off at nine volts. Part B wants to find the time constant how the physical to our time, see and use the equation for the voltage in a capacitor when it's charging. So v c musical to bolt is in the battery times one minus you to the minus t over R C from the graph. If you say at T equals toe one second, then we get the voltage in the capacity to be four months now with this information on you to do is not solved for our time seen so the viable side by the voltage in the battery and now we have we see well, everybody is equal to one minus e to the minus t over our see subtract the one we have the sea over absolutely bolting the battery like this one. Tu minus e to the minus t over our See Now if we just plug in the numbers for the voltage in the capacitor and bolted to the battery just to simplify a little bit, we have receiving her for the water by nine minus the one. So we go minus minus 59 Now we can plug that in, and if we get rid of the negative on the right side, we just have five nights positive. 5/9. Physical to E to the minus. G over. Arm. See. So now we take the natural log rhythm of both sides to get rid of that exponential. We have Ellen have all nine physical to L A and e to the minus T R c well, and of e Ellen of years one. So that was the way. So we're left with Ellen. I have. Ninth is equal to minus t over our I see. That's for looking for our time. See, you multiply both sides by our time sitting and divide by the Eleanor five or nine to get R C. Which is the time constant is equal to minus t over. Ellen five nights. So just plug in your T value, which we took as one. What's minus one over Ellen by nights. So for a time, constant town just quickly R. C is people too. 1.71 seconds. Now, with that information, we can find the answer to part See, so we're looking for is the capacitance. So we know R. C is equal to 1.71 So it's all or C. We get C is equal to 1.71 that of my arm. And we know our that was given to us earlier. So it's 1.71 divided by 4000 700. So for part, see, capacitance C is equal to 0.36 I was 10 to the minus six the Reds.

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