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Each shot of the laser gun most favored by Rosa the Closer; the intrepid vigilante of the lawless 22nd century, is powered by the discharge of a 1.19 F capacitor ch...

Question

Each shot of the laser gun most favored by Rosa the Closer; the intrepid vigilante of the lawless 22nd century, is powered by the discharge of a 1.19 F capacitor charged to 64.1 kV. Rosa rightly reckons that she can enhance the effect of each laser pulse by increasing the electric potential energy of the charged capacitor: She could do this by replacing the capacitors filling, whose dielectric constant is 467, with one possessing a dielectric constant of 941.Find the electric potential energy U1

Each shot of the laser gun most favored by Rosa the Closer; the intrepid vigilante of the lawless 22nd century, is powered by the discharge of a 1.19 F capacitor charged to 64.1 kV. Rosa rightly reckons that she can enhance the effect of each laser pulse by increasing the electric potential energy of the charged capacitor: She could do this by replacing the capacitors filling, whose dielectric constant is 467, with one possessing a dielectric constant of 941. Find the electric potential energy U1 of the original capacitor when it is charged: Calculate the electric potential energy Uz of the upgraded capacitor when it is charged. U2



Answers

In The NOVA laser fusion experiment at Lawrence Livermore Laboratory in California uses energy at the rate of $10^{14} \mathrm{~W}$ (roughly 100 times the output of all the world's power plants) while its lasers are on. However, one laser pulse lasts for only $10^{-9} \mathrm{~s}$. (a) Only about $0.17 \%$ of the capacitor energy actually appears as light. How much light energy is delivered in one pulse? (b) The capacitor bank supplying this energy has a total capacitance of $0.26 \mathrm{~F}$. What's the potential difference across the capacitor bank when it's fully charged?

So for question A. We know the energy store equation is probably won't have time. See, test out of the square that was the under store and seized a capacitance, which is given 61 times. Tend to apartment three para The potential difference. Tell that B C equals the tempo. No kill boats, which is 10 times 10 to the power three boats because one kilowatts is 10 to the power three both. Okay, so if we plug in these batteries back into them pushing, we have energy stored out. You see, for two well half times 61 tends tends apartment every three Sarah and then times can times potential power Three boats enable square here, and this will give us and energy stories about during point. Cofie times tend to a part of six You for question would be It was asking us to determine in power. So we know the power is equal to energy store. You buy time so we know the energy from the last question, which is 3.5 potential problem. 62 The times given is $10 seconds, which is 1.1 times tensile pollinated 80 seconds. Therefore, we have power is equal to three point. So if I times tens of our six you over one or no times tens of power negative a second and this would give us the power is about three point over. I times tend to a bar of 14. What's and for the last question was asking us the time exactly. OK, so we know the time single toe end restored about divided by the power. So the end of story is given as £3.5.10 to part six to the power in this case is given as one point killed lots, which is 1000 watts. Therefore, Time t can you go to, uh, 3.0 If I times tend to about six ju over 1000 watch and this will give us the times about three point Joe, if I times 10 to the power of three second, which is 30 50 seconds. Okay. And these are the answers for these questions. Thank you.

Okay. The question asks us to find how much energy you can be stored in capacitor when the applied voltage is 25. Love won't. So energy stolen capacitor is given by huff. See, be square. That is capacitance time square off the voltage. So how time see his point zero eight zero times 10 power. Negative six. Now voltage applied is 25 kilo boat, so it's 25 1000 square. Not if you multiply this you will get the answer. 25 jewels? No. The next part of the question is to find out the power off the laser posts. No, our is equal to Delta e divided by Delta t that his energies given divided by the time required to give that energy. Now it says that this energy stored in capacitor that is 25 jewels is used, but not fully only 15% off it is used. So you want to multiply here by 0.15 Get to get the actual energy divided by Delta team, which is four microseconds. That is full times 10 power, negative six. So answer to this question is nine 30 7.5 killer. What? That is Kellerman's 1000. So on dhe, we want only to significant digits. So you will keep 9 40 your approximate the answer to 9 40 killer, but

Not in this problem. It is given there is a cap pistol off, Captain Strains. Why did no pipe my property? It is to be converting to pet it in the later nitrogen. There is a cap, Mr Off. This better? No, it is to be charts Max. Simple Dangel up, but 30 global How? Convert this value into wood 30,000 in the first part. We have to calculate in order to store in the tapestry energy stored in the captain's chair be a point which could be measured by the formula. Ha! Busy until they have you guys square. Now we're going to subject of the value of cap pistons. Toby, why you don't fight my professor it But we have converting to ferret. Our transit is 30,000 fold on. Simply play. But energy started The tapestry would be Forget radio. So this is your quest part and second project is given him percent off. Energy up capital. Well, person talk energy off campus today it's closing the ledge. So energy off like you may cancel it. Great person. Go. I don't get to do on this Energy spills in the diamond. Debelo it microsecond. That is Hey, you can do the part by the six second. So But what about the little beer to cooperate Father is in order to produce. But in that time, no such event. 1% off quantity. The 12 into 23 diverted by 100. That with a good percent often poetry and time. Interval is if you can't do the important by the six. So this would be 3.4 and you can use the power fight were so probably the laser beam is three point put into 10 to the power bi foot. This is the under part this program.

So, given that a power supply has a capacitance sea of 0.5 micro fare ads, or we can rewrite that as 5.0 times 10 to the minus eight fair at Since one micro fair at has tended to minus six fare ads and a voltage maximum voltage be of 35 kilovolts or 3.5 times 10 of the four volts. And there's 10 to the third, uh, volts in every kill a bull. So a A wants us to estimate how much energy could be stored in this capacitor. Well, the energy store, Well, this is part, eh is found using the fact that P E for potential energy or energy stored, is equal to 1/2 times the capacitance of the capacitor times the voltage squared. So plugging those values and its expression, we find that this is equal to approximately 31. Jules. The box said it is a solution for a part. B wants us to find the power output of this will. The power output is the energy power potential. Energy power is equal to the energy divided by the time of that output. Okay, well, it says that the time here is considered to be 6.2 microseconds, or 6.2 times 10 to the minus six seconds, and only 12% of the potential energy is going to be converted into use energy. So 12% 0.12 times the potential energy. So 0.12 is multiplied by P. E, divided by the time out for it, which was 6.2 times 10 to the minus six seconds. Plugging those values into this expression, we find that this is able to 5.9 times 10 to the fifth in the units here are walks, so w box it in is her solution to the question.


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