According to the official web site, the Z Machine emits a peak power of 3.5 time

Question

According to the official web site, the Z Machine emits a peak power of 3.5 times 10^14 W (350 terawatts), has a total energy output of 2.7 times 10^6 J (2.7 megajoules) n the form of X-rays, using a maximum current of 2.6 times 10^7 A (26 megamps) and a peak potential of 1.0 times 10^5 V. These numbers are from the official site, so they are probably trustworthy. The power is supplied by a huge capacitor bank, containing 80 capacitors in parallel, each rated at 0.040 F and rated safe to operate a 1.0 times 10^5 V. The total resistance of the system is given as 0.10 ohm. Assume all values are correct to two significant figures. For more on the Z-Machine, see http: //www.sandia.gov/z-machine/ http: //www.sandia.govwiz-machine/about zindex.html/ http: //www.sandia.gov/media/zpinch.htm/ http: //fire.pppl gov/fpa05_olson.pdf http: //www.physicscentral.com/explore/action/fusion.cfm http: //en.wikipedia.org/wiki/Z_machine#Prospects http: //en.wikipedia.org/wikicapacitor#Pulsed_power_and_weapons http: //nextbigfuture.com/2011/02/z-pinch-roadmap-to-petawatts-and-beyond.html a. How much energy could be stored in all those capacitors if they all were charged to the maximum 1.0 times 10 degree V? b. Find the time constant of the capacitor discharge, if all of the capacitors are in parallel and made to behave as one huge capacitor. c. In reality, the capacitors are arranged so that each one contributes separately to the total energy making the characteristic time shorter. Find the time constant of the capacitor discharge, if each capacitor is considered separately. d. If all of the X-ray energy (NOT the energy calculated in Part a) were used at the peak power rate (assuming that rate to be constant), how much time would be required to deliver all that energy? e. At the maximum current at the resistance given above, find the voltage using Ohm's Law. F. (the hard part) Obviously there are discrepancies between your calculations and what the ordinary laws of electricity and energy would lead you to expect. That's because there are other complex processes occurring for which we can't account. So we'll try something else. If the capacitors are fully charged and storing the amount of energy calculated in Part a, how much time will be required to discharge a total energy of 2.0 times 10^9 J into the system?

Explanation / Answer

2) N = 80 ; F = 0.04 F ; V = 1 x 10^5 V ; R = 0.1 Ohm

a)Since all the capacitors are connected in parallel, the equivalent capacitance is:

C = 80 x 0.04 = 3.2 F

we know that, stored energy of capacitor is given by:

U = 1/2 C V^2

U = 0.5 x 3.2 x (1 x 10^5)^2 = 1.6 x 10^10 J

Hence, U = 1.6 x 10^10 J

b)We know that the time constant is given by:

time constant = t = RC = 0.1 x 3.2 = 0.32 s

Hence, t = 0.32 s

c)For one capacitor, C = 0.04 F

time constant = t = RC = 0.1 x 0.04 = 0.004 s

Hence, t' = 0.004 s

d)E = 2.7 x 10^6 J

P = 3.5 x 10^14 W

from the defination of power ; P = E/t

t = E/P = 2.7 x 10^6/3.5 x 10^14 = 7.71 x 10^-7 s

Hence, t = 7.71 x 10^-7 s

e)we know that

P = V^2/R => V = sqrt (P R)

V = sqrt (3.5 x 10^14 x 0.1) = 5.9 x 10^6 V

Hence, V = 5.9 x 10^6 V

f)t = E/P

t = 2 x 10^9/3.5 x 10^14 = 5.71 x 10^-4 s

Hence, t = 5.71 x 10^-4 s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.