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:(adsbygoogle = window.adsbygoogle || []).push({});

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 = (u_{0}N^{2}A)/l

where L = inductance in Henry

N = number of turns

A = area of cross-section

l = length in meters

L = (4*(pi)*10^{-7})(545^{2})(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*I^{2}

where U = energy

L = inductance

I = current

U = 0.5*(7.66 *10^{-4})*(1.25^{2})

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 = U_{0}e^{-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?

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# Homework Help: Current Decay in an R-L Circuit

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