06 Dec '12 02:432 edits

Just trying to put together a analytic model for how long it may take to drain battery by means of a simple resistor...hitting some "walls" so to speak, and was hoping for some input.

So im assuming the work a battery can do is given by (1)

Where

W= Work the battery can do

Q = charge the battery holds

V = voltage across the terminals

W = Q*V (1)

taking the time rate of (1) -->(2)

dW/dt = Q*dV/dt + V*dQ/dt (2)

Using ohms law (3)

V = i*R (3)

taking the time rate of (3) (assuming "R" remains constant and dV/dt is negtive) --> (4)

dV/dt = -R*di/dt (4)

substitute (4) into (3) -->(5)

dW/dt = -Q*R*di/dt + V*dQ/dt (5)

At (5) things get fuzzy for me, I could substitute

di/dt = d^2Q/dt^2, or dQ/dt = i (which I think would be the better choice) yeilding

dW/dt = -Q*R*di/dt + V*i

or

dW/dt = -Q*R*d^2Q/dt^2 + V*dQ/dt

But I cant figure out what to do with V or Q, and what dW/dt is as a function?

It could be that I don't know jack about circuit analysis and MAYBE the whole thing needs to be scrapped...I don't know?

So im assuming the work a battery can do is given by (1)

Where

W= Work the battery can do

Q = charge the battery holds

V = voltage across the terminals

W = Q*V (1)

taking the time rate of (1) -->(2)

dW/dt = Q*dV/dt + V*dQ/dt (2)

Using ohms law (3)

V = i*R (3)

taking the time rate of (3) (assuming "R" remains constant and dV/dt is negtive) --> (4)

dV/dt = -R*di/dt (4)

substitute (4) into (3) -->(5)

dW/dt = -Q*R*di/dt + V*dQ/dt (5)

At (5) things get fuzzy for me, I could substitute

di/dt = d^2Q/dt^2, or dQ/dt = i (which I think would be the better choice) yeilding

dW/dt = -Q*R*di/dt + V*i

or

dW/dt = -Q*R*d^2Q/dt^2 + V*dQ/dt

But I cant figure out what to do with V or Q, and what dW/dt is as a function?

It could be that I don't know jack about circuit analysis and MAYBE the whole thing needs to be scrapped...I don't know?