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sdalglish13
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I was trying to solve this problem the other day for my physics class and I keep getting the wrong answer. The problem is as follows:
An ideal solenoid is 18.5 cm long, has a circular cross-section 2.20 cm in diameter, and contains 545 equally spaced thin windings. This solenoid is connected in a series circuit with a 15 ohm resistor, a battery of internal resistance ohms and open-circuit terminal voltage of 25 V, and an open switch. (Note u = 4*(pi)*10-7 T *m/A)
How long after closing the switch will it take for the stored energy in the solenoid to reach 1/2 of its maximum value?
So this is what I did:
L = (u0N2A)/l
where L = inductance in Henry
N = number of turns
A = area of cross-section
l = length in meters
L = (4*(pi)*10-7 )(5452)(3.8*10-4)
.185
L = 7.66 *10-4 H
Then I found the current I:
I = emf/R
where emf = electromotive force/voltage
R = resistance
I = 25 Volts/(15 ohms + 5 ohms) = 1.25 Amps
Next I used the energy equation to find the maximum energy:
U = 0.5*L*I2
where U = energy
L = inductance
I = current
U = 0.5*(7.66 *10-4)*(1.252)
U = 5.99*10-4 J
Then I don't know where to go from there to find time. I already tried an equation I found in my textbook...
U = U0e-2*(R/L)*t
t = -ln(.5)*L/(2R)
t = -ln(.5)*(7.66 *10-4)/(2*(15+5))
t = 1.32*10-5 sec
and solved for t that way, but I keep getting 1.32*10-5 sec, when the answer should be t = 4.71 *10-5. I know t = 4.71 *10-5 is the correct answer because it came off of the answer sheet for a review.
Can anyone shed some light on what I am doing right/wrong?
An ideal solenoid is 18.5 cm long, has a circular cross-section 2.20 cm in diameter, and contains 545 equally spaced thin windings. This solenoid is connected in a series circuit with a 15 ohm resistor, a battery of internal resistance ohms and open-circuit terminal voltage of 25 V, and an open switch. (Note u = 4*(pi)*10-7 T *m/A)
How long after closing the switch will it take for the stored energy in the solenoid to reach 1/2 of its maximum value?
So this is what I did:
L = (u0N2A)/l
where L = inductance in Henry
N = number of turns
A = area of cross-section
l = length in meters
L = (4*(pi)*10-7 )(5452)(3.8*10-4)
.185
L = 7.66 *10-4 H
Then I found the current I:
I = emf/R
where emf = electromotive force/voltage
R = resistance
I = 25 Volts/(15 ohms + 5 ohms) = 1.25 Amps
Next I used the energy equation to find the maximum energy:
U = 0.5*L*I2
where U = energy
L = inductance
I = current
U = 0.5*(7.66 *10-4)*(1.252)
U = 5.99*10-4 J
Then I don't know where to go from there to find time. I already tried an equation I found in my textbook...
U = U0e-2*(R/L)*t
t = -ln(.5)*L/(2R)
t = -ln(.5)*(7.66 *10-4)/(2*(15+5))
t = 1.32*10-5 sec
and solved for t that way, but I keep getting 1.32*10-5 sec, when the answer should be t = 4.71 *10-5. I know t = 4.71 *10-5 is the correct answer because it came off of the answer sheet for a review.
Can anyone shed some light on what I am doing right/wrong?