Problem

An $R L C$ circuit has a capacitance of 0.29$\mu …

04:47

Problem 68 Medium Difficulty

An RLC circuit has a resonance frequency of 155 Hz. (a) If both $L$ and $C$ are doubled, does the resonance frequency increase, decrease, or stay the same? Explain. (b) Find the resonance frequency when $L$ and $C$ are doubled.

Answer

a) see explanation
b) 77.5 $\mathrm{Hz}$

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Physics 102 Electricity and Magnetism

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Video Transcript

in the first item, we change our setup to another one. We have a capacitance see prime because 22 times see and I in victims l prime equals to two times El And then what will happen to that resonant frequency under that change? So the resonant frequency is given by one divided by two pi times the square it off l time see number four. After the change, our resident frequency F prime will be equals through one divided by two pi times the square root off l PrimeTime See prime. No. Using these information, we get that our new frequency will be f crime that easy coz true to buy times the square root off four l c under one No stats that denominator have increase it because of that change, then the frequency will decrease after that change in there for the answer to the first item is that the resonant frequency will decrease after changing both the capacitor on Dr No on the second item, we have to actually calculate what is that new resonant frequency when a terrible both being booked us on the capacitance and it's very easy to do by using these expression. We can find a relation between both both resonant frequencies. F prime is equals two too quiet times too, Because we have a square it off more. Here, I'm the square root off l time see under one that we can recognize. These terms here has bean the old, resonant frequency. Then the new resonant frequency is he goes to the old resonant frequency divided by two which is equals to 155 divided by two and easiest 7 to 7 0.5 hertz.

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