The high energy collider at FermiLab in Chicago uses a bank of capacitors that c
ID: 1623286 • Letter: T
Question
The high energy collider at FermiLab in Chicago uses a bank of capacitors that can deliver 360 MW of power to ramp-up an electromagnet during particle collisions. If the capacitor tree consists of 864 capacitors, each 1F, fully charged to 400 V, and connected in parallel, how long will it take the tree to discharge to half its original voltage through a 0.95 Ohm load resistance? Show your work. Select the best answer or completion to each of the questions or incomplete statements below. Consider the circuit below, if another resistor and another capacitor were both added to the circuit in series, how would the time constant of the circuit change? A. Increase B. It depends on the size of each. C. Decrease D. Stay the same E. Increase only for small voltagesExplanation / Answer
864 capacitors with capacitance of 1F are connected in parallel connection.
Ceq = 864 x 1 = 864 F
T = R Ceq = 820.8 s
V = Vo [ e^(-t/T)]
0.5 Vo = Vo [ e^(-t / 820.8)]
- t / 820.8 = ln(0.5)
t = 569 sec or 9.48 minutes
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1. Req = R + R = 2 R
1 / Ceq = 1/C + 1 /C
Ceq = C/2
time constant = Req Ceq = (2R) (C/2) = R C
(D) stays the same.
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