Maximum rate at which energy is stored in a LR circuit

[Serotonin]

Homework Statement

An Inductor L and a Resistance R are connected in series with a battery of emf E. Find the maximum rate at which the energy is stored in the magnetic field.

Homework Equations

Energy stored in an inductor : U= 1/2Li²
For a simple LR circuit with a DC voltage source the equation of current at some time t is I= I_max(1-e^-Rt/L)
So plugging in the value of current in the energy stored inside an inductor equation and differentiating it with respect to time we will get the equation of Power in a simple LR circuit as a function of time.

The Attempt at a Solution

So I solved for the the maximum power by differentiating the Power equation once again wrt to time and equated it with zero to get the time at which the power transfer would become maximum. I once again plugged in the value of time to get the maximum power to get what is asked in the question. But unfortunately I'm getting the answer as zero which is not correct. I don't know where I'm going wrong.

 

[cnh1995]

Welcome to PF!

Please show your working so that we can see what went wrong.

 

[Serotonin]

OK I am trying to attach the pictures but it is not working

 

[Serotonin]

Hey would it be inappropriate to attach pics since the solution involves a number of integrals?

 

[cnh1995]

OK I am trying to attach the pictures but it is not working

Try the "upload" button below.

Hey would it be inappropriate to attach pics since the solution involves a number of integrals?

It is better to type the equations instead of posting images. If you want to post the images, make sure they are clear and easy to read.

 

[gneill]

Hey would it be inappropriate to attach pics since the solution involves a number of integrals?

You may attach pictures showing your work if they are clearly legible and well organized (pictures of scratch workings randomly scattered over a piece of paper with other problem's workings are obviously going to be rejected and deleted by moderators). Get into the habit of numbering all the equations in images so that helpers can reference them when discussing the work.

A much better approach is to learn to use LaTeX syntax to present your work. Then there will never be an issue with clarity and helpers can quote and comment on individual elements of the work easily. See the link: https://www.physicsforums.com/help/latexhelp/

 

[Serotonin]

Thanks for guiding me. My problem has been solved. Actually I was making a silly mistake.
Nice to meet you.

 

[Serotonin]

Hey what to do when you want to close the thread?

 

[Serotonin]

You may attach pictures showing your work if they are clearly legible and well organized (pictures of scratch workings randomly scattered over a piece of paper with other problem's workings are obviously going to be rejected and deleted by moderators). Get into the habit of numbering all the equations in images so that helpers can reference them when discussing the work.

A much better approach is to learn to use LaTeX syntax to present your work. Then there will never be an issue with clarity and helpers can quote and comment on individual elements of the work easily. See the link: https://www.physicsforums.com/help/latexhelp/

Thanks mate!

 

[gneill]

Hey what to do when you want to close the thread?

There's nothing you need to do to close it; we generally don't close threads unless there's an extraordinary reason.

You may click the "MARK SOLVED" button at the top right of the thread if you wish to indicate that you're satisfied with the results of the discussion.