# Why does i(t)=dq(t)/dt give the value of AC current only?

I know the mathematical and geometrical reason, but does there exist a physical interpretation behind this?

Thanks f95toli
Gold Member
I am not sure what you mean.
That formula works for DC as well. An "exotic" example would be a single electron pump where the (dc) current is given by the number of electrons pumped per second...

I am not sure what you mean.
That formula works for DC as well. An "exotic" example would be a single electron pump where the (dc) current is given by the number of electrons pumped per second...

I don't believe it does. Say that a constant 10 Coulombs of charge per second is flowing through a conductor. This would be equivalent of 10 Amps of current. The rate of change in Coulombs per second is zero. So the equation i(t)=dq(t)/dt would yield zero also.

Andrew Mason
Homework Helper
I don't believe it does. Say that a constant 10 Coulombs of charge per second is flowing through a conductor. This would be equivalent of 10 Amps of current. The rate of change in Coulombs per second is zero. So the equation i(t)=dq(t)/dt would yield zero also.
!? The rate at which charges move is dq/dt. That is the current. You appear to be confusing dq/dt with d2q/dt2. The rate of change of charge flow is not the same as the rate of charge flow.

AM

This would be equivalent of 10 Amps of current.

No, it is 10 amps of current.

!? The rate at which charges move is dq/dt. That is the current. You appear to be confusing dq/dt with d2q/dt2. The rate of change of charge flow is not the same as the rate of charge flow.

AM

Say at t = 2 seconds there is 10 Coulombs flowing in the conductor, at t = 3 seconds there is 10 Coulombs flowing in the conductor. A simplified way of figuring dq/dt would be (10 - 10) / (3 - 2) = 0. A slope of a horizontal line is always zero.

d2q/dt2 is the rate of change of the rate of change.

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Say at t = 2 seconds there is 10 Coulombs flowing in the conductor

There is or there are?

But no, there are 10 coulombs per second flowing.

If you re-examine your units you will understand what everyone is telling you.

I don't believe it does. Say that a constant 10 Coulombs of charge per second is flowing through a conductor. This would be equivalent of 10 Amps of current. The rate of change in Coulombs per second is zero. So the equation i(t)=dq(t)/dt would yield zero also.

It helps if you think in terms of current DENSITY at first:
J = ρ.v = ρ.(dx/dt)

Now consider a cross-section of your conductor and perform a surface integral, the result:
I = (dq/dx) (dx/dt) = dq/dt

So the proper interpretation of the dq/dt term is the rate of charges that cross a certain reference surface. So even for a DC current of, say, 10 A, then every second 10 C cross that surface.

There is or there are?

But no, there are 10 coulombs per second flowing.

If you re-examine your units you will understand what everyone is telling you.

OK I get it now. I was thinking in terms of current flow, not charge flow. At t=2, 20 coulombs have flown through a conductor. At t=3 30 coulombs have flown through a conductor. So (30 - 20) / (3 - 2) = 10 coulombs per second. The coulomb count is accumulative.

Sorry for the confusion (and bad grammar) - watching a two-year old can cause a lack of concentration.

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