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1-0u-VF capacitorconnecteoDartery How much eneroystoredthe capacitor?Had the capacito Deen connectedOo-V battery nowy much energy woulc havebeen stored?...

Question

1-0u-VF capacitorconnecteoDartery How much eneroystoredthe capacitor?Had the capacito Deen connectedOo-V battery nowy much energy woulc havebeen stored?

1-0u-VF capacitor connecteo Dartery How much eneroy stored the capacitor? Had the capacito Deen connected Oo-V battery nowy much energy woulc havebeen stored?



Answers

A capacitor has a charge of $2.5 \mu \mathrm{C}$ when connected to a 6.0 -V battery. How much energy is stored in this capacitor?

So we have a capacitor with the three Micro fared capacitance, and that's connected to a 12 volt battery. And we're looking for how much energy is stored in the capacitor. So this is V, uh, the energy is you, which is 1/2 C V squared. And this looks like a lot of different forms of potential energy. One halftime something times something else squared. So for this set up, uh, we have 1/2 times three, and it's in micro fared. So that's times 10 to the negative. Sixth and 12 volts squared. And this is 2.16 times 10 to the minus four. And the unit is Jules. Because we're energy now. What happens when we have the same capacitance? But instead we change the voltage to six folds? Well, the voltage is squared in the equation. So for taking half the voltage, we should get 1/4 the energy eso. We can do the same thing 1/2 times. See, times V is now six, and that's squared. We get 5.4 times 10 to the minus fifth, and that's in jewels as well and 5.4 times 10 to the minus fifth is 1/4 of 2.16 times, 10 to the minus four. So where answer makes sense?

So this question belongs to the electric potential and potential energy in which we have a child's Q equals to eight million column which is located at the origin. And calculate the work done W in taking a small charge of small Q equals two minus two molecular bait. And to the power minus nine column from point P. That is equal to zero comma zero comma three centimeter. Who a point Q. Which is zero comma four centimeter comma zero via point capital are that is equal to zero comma six centimeter comma nine centimeters. So we have to calculate the work done to take this job queue from point P to point Q. Okay. And we know that the wagon is dependent on the initial and final situation. So there is no role of this point. Okay. There is no role of this point because the work done will be dependent on the initial and the final situation. Okay, So we can write that the work done W. This will be equals to charge Q manipulated a potential difference. So potential difference will be we two minus 31 Okay. And potential difference is due to this chart. Okay, so we can write that Q. And potential difference we to it will be equals two K. Q divided by de tu minus Q. Sorry, this will be the capital Q charts. Okay. And this will be also capital future because capital futures is creating potential here. Okay, so substituting all the values of ogden W. It will be small charge Q which is a small Q. So small Q is equal to minus two. More player by 10 To the power minus nine Fulham. And from here we can take out this K and Q commons Okay, which is 19 to 10 To the power nine Marbler by capital Q. Which is this value? So eight million column that is eight molecular bait. And to the power minus three and one by D two D two will be this value four centimeter and four centimeter can be converted into meter by multiplying by 10 to the power minus two and minus one by devon. Devon is the initial position, which is three centimeters, so three multiplied by 10 to the power minus two m. Okay, so from here, after solving this completely, we get work done. W this is equal to 1.27 jewels. Okay, so this is the answer for this question. Okay, so this much of what is needed for this process. Okay.

So this question belongs to the capacitor in which we have a capacitor of composite and Sequels to 12 PICO fairer. That is equal to 12 montclair bait. And to the power minus 12 ferret. Okay. And it is connected to a Battery having potentially equals to 50 world. So we have to determine how much electrostatic energy is stored in the capacitor. That is you capital? You Okay. So we know that the energy store by the capacitor in the form of electrostatic energy. It is equals to one by to see we square were seized the capacitance and we use the potential connected. So we're substituting values. So one by two manipulated by sea Which is 12 more player bait. And to the power managed to welfare or player baby which is 50 rolls of 50 world. Holy Square. Okay. And from here after solving we get U. Equals to 1.5 molecular by 10. To the power minus eight jewel. So this becomes the answer for this question and this much of energy is being stored by the capacitor at this 50 world potential difference. Okay.

We're going to find the energy stored in a capacitor of 4.5 micro fair days with 12V connected across it. So that the calculation for potential energy, electrical potential energy and a capacitor Is 1/2 the charge on it times the potential difference. And usually people substitute in the definition of capacitance Q is equal to see delta v. And then get that that potential energy is one half C delta v squared. And just a note, um when we looked at fields, we said that electric potential energy is the charge Q. Sitting at a potential difference V. So that is a single point charge sitting in an external field of some sort. But you may have a question about where the one half factor comes from. And it's because you're building up potential energy by adding more and more charge. So if you look at uh the charge versus potential difference across the plates that grows in a linear way as you build up potential and the energy is the area under that graph. So the fact that you're building up a charge Piece by piece gives you that factor of 1/2 based on the area under the build up curve. But anyway, it's a fairly straightforward calculation to do What half c. In this case is 4.5 types 10 to the -6 Faraday's and then 12 old squared the units being an S. I will give us jules. Mhm.


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