Intigrated problem 84) The highest magnetic fields in the world are generated wh

Question

Intigrated problem 84)

The highest magnetic fields in the world are generated when large arrays, or "banks", of capacitors are discharged through the copper coils of an electromagnet. At the National High Magnetic Field Labrotory, the total capacitance of the capacitor bank in 32mF. Theres capacitors can be charged to 16kV.

A) What is the energy stored in the capacitor bank when it is fully charged?

B) When discharged, the entire energy from this bank flows through the magnet coil in 10ms. What is the average power delivered to the coils during this time?

Explanation / Answer

a.) Energy stored in a capacitor E = 0.5 C V2 , where C is the Capacitance and V is the Voltage across the capacitor

C = 32 mF = 32 x 10 -3 F (given)

When full charged V = 16 KV = 16000 V ,

Therefore E = 0.5 x 32*10-3 x 160002 = 4096000 J or 4096 KJ

b.) Power delivered = Energy transfered / time taken

P = E /t

time t = 10 ms = 10 x 10-3 s = 0.01 s

Therefore, P = 4096000 / 0.01 = 409600000 W

Average power delivered = 409.6 x 106 W or 409.6 MW

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