LR Circuit: Solving for Charge Flow?

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The discussion revolves around solving for charge flow in an LR circuit, specifically addressing the integration of current over time. The current is expressed as i = i_o (1 - e^{-t/τ}), where τ = L/R. The user is struggling with integrating dq/dt = i_0 (1 - e^{-t/τ}) to find the charge. Despite attempts, the integration is not yielding the correct result. The solution is suggested to be straightforward by integrating dq/dt with respect to time.
cupid.callin
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I solved it :p

Homework Statement


attachment.php?attachmentid=33120&stc=1&d=1300218625.jpg

The Attempt at a Solution



I need help with part (a)

Current in LR circuit, i = i_o (1 - e^{-t/\tau}) and \tau = \frac{L}{R}

so, \frac{dq}{dt} = i_0 (1 - e^{-t/\tau})

integrating it is not giving me the correct answer.
 

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cupid.callin said:
I solved it :p


Homework Statement


attachment.php?attachmentid=33120&stc=1&d=1300218625.jpg



The Attempt at a Solution



I need help with part (a)

Current in LR circuit, i = i_o (1 - e^{-t/\tau}) and \tau = \frac{L}{R}

so, \frac{dq}{dt} = i_0 (1 - e^{-t/\tau})

integrating it is not giving me the correct answer.

just integrate with respect to t, dq/dt = ... dq = ...dt
 
its solved ... i wrote it on the top
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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