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# Proof that current is the rate of change of charge with respect to time

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1. I've been looking for a proof of this but its impossible to find one.
Ive started with the fact that E=QV
therefore dQ/dt=d(E/V)/dt
dE/dt= power = P= IV
but I'm stuck with derivative of voltage.
I know quotient rule will help.

thanks
2. (Original post by kennz)
I've been looking for a proof of this but its impossible to find one.
Ive started with the fact that E=QV
therefore dQ/dt=d(E/V)/dt
dE/dt= power = P= IV
but I'm stuck with derivative of voltage.
I know quotient rule will help.

thanks
Instead of using calculus, you could just use normal equations:
and
Equate the two equations for E:

Cancel the voltages off both sides after combining:

So current is change in charge, respect to time.
3. (Original post by The-Spartan)
Instead of using calculus, you could just use normal equations:
and
Equate the two equations for E:

Cancel the voltages off both sides after combining:

So current is change in charge, respect to time.
Thankk you for that, is there not a way to do it with calculus though?

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