The highest magnetic fields in the world are generated when large arrays, or \"b
ID: 1260862 • Letter: T
Question
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 Laboratory, the total capacitance of the capacitor bank is 32 mF. These capacitors can be charged to 16 kV.
What is the energy stored in the capacitor bank when it is fully charged?
When discharged, the entire energy from this bank flows through the magnet coil in 10 ms. What is the average power delivered to the coils during this time?
Explanation / Answer
The energy stored in the capacitor tank is
E = 1/2 CV2
Here, capacitance of the capacitor is C and potential difference is V.
Subsitute 32 mF for C and 16 kV for V in the above equation
E = 1/2 CV2
= 1/2 (32 mF)(10-3 F/ 1 mF)(16 kV)2 (103 V / 1 kV)2
= (4096 x 103 FV2)( 1 J / 1 FV2)
= 4096 x 103 J
The average power delived to the coil is
P = E / t
Here, time taken by the bank to flow energy through the magnetic coil is t.
Subsitute 4096 x 103 J for E and 10 ms for t in the above equation
P = E / t
= 4096 x 103 J / (10 m) ( 10-3 s / 1 ms)
= (4096 x 105 J/s) ( 1 W / 1 J/s)
= 4096 x 105 W
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.