Question

1 Figure 31-19 shows three oscillating LC circuits with identical inductors and capacitors. At a particular time, the charges on the capacitor plates (and thus the electric fields between the plates) are all at their maximum values. Rank the circuits according to the time taken to fully discharge the capacitors during the oscillations, greatest first. (a) (b) (c) Figure 31-19 Question 1. ?² = 1/LC

          1 Figure 31-19 shows three oscillating LC circuits with identical inductors and capacitors. At a particular time, the charges on the capacitor plates (and thus the electric fields between the plates) are all at their maximum values. Rank the circuits according to the time taken to fully discharge the capacitors during the oscillations, greatest first.
(a) (b) (c)
Figure 31-19 Question 1.
?² = 1/LC

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1 Figure 31-19 shows three oscillating LC circuits with identical inductors and capacitors. At a particular time, the charges on the capacitor plates (and thus the electric fields between the plates) are all at their maximum values. Rank the circuits according to the time taken to fully discharge the capacitors during the oscillations, greatest first.
(a) (b) (c)
Figure 31-19 Question 1.
?² = 1/LC

Added by Kaitlin W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Titus Dascalu

05/14/2022

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Since the inductors and capacitors in all three circuits are identical, the resonant frequencies of the circuits are also identical. Show more…

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Figure 31-19 shows three oscillating LC circuits with identical inductors and capacitors. At a particular time, the charges on the capacitor plates (and thus the electric fields between the plates) are all at their maximum values. Rank the circuits according to the time taken to fully discharge the capacitors during the oscillations, greatest first. Figure 31-19 Question 1. ω² = 1/LC

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Transcript

0:00 Hi.

00:01 So this is a nice question because it requires us to study three different circuits, but they're both very simple.

00:09 All of them are very similar because they are three oscillating alc circuits, so circuits that contains inductors and capacitors.

00:18 So let me try to sketch the circuits very quickly.

00:22 So one has an inductor and a capacitor.

00:24 The other one has the same inductor, but it has two capacitors linked in parallel.

00:31 We assume that the capacitors are identical.

00:34 And the third circuit, which has the same inductor, and the same two capacitors, but this time linked in series.

00:44 So let's call them a, b, and c.

00:48 We also know from the question that the frequency of these oscillating capacitors, so the frequency squared, is given by 1 over l, c, where l is the total inductance of the circuit and c is the total capacitance of the circuit.

01:04 And we have to order the three circuits or to rank them according to the time taken to fully discharge the capacitors during the oscillations.

01:13 So we know that the capacitors will discharge in half a period or one period.

01:19 So this means that the circuits which will discharge quicker are the circuits with a higher frequency.

01:26 So basically we have to order these three circuits in decreasing, in terms of their decreasing frequency.

01:38 So for the first circuit a, omega a squared will be simply given by 1 over lc.

01:45 If we assume that the inductor has an inductance l and the capacitor has a capacitor c...

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