Current: Average vs. Instantaneous.

[sweetreason]

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A silver wire 2.6mm in diameter transfers a charge of 420 C in 80min . Silver contains 5.8*10^28 free electrons per cubic meter.

What is the current in the wire?
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I have correctly solved this problem using I= Q/t, but I am a bit confused by this. Correct me if I'm wrong, but this is the formula for *average* current. I thought that in general, I= dQ/dt, and that only in cases when you have a complete circuit is the current the same everywhere. In this special case, the average current would be equal to the instantaneous current, but we are not given that we have a complete circuit. So why do we use the formula for average current?

Thanks!

 

[vela]

You're not given enough information to find the instantaneous current, so you need to make a simplifying assumption that the current is constant.

Another way of looking at it is that time intervals corresponds to average quantities while particular instants correspond to instantaneous quantities. It generally wouldn't make sense to ask for the average current at t=0 s or for the instantaneous current from t=0 s to t=1 s. It does make sense, on the other hand, to ask for the average of the current over the time interval t=0 s to t=1 s, or to ask for the current at the instant t=0 s. The problem statement gives you a time interval of 80 minutes, so the only current you can find is the average current. If you were supposed to find an instantaneous current, you'd have to be given a particular instant in time for which to find the current.