Question

The current through a wire depends on time as i=(2+3t)A. Calculate the charge crossed through a cross section of the wire in 10sec.

Answer 1

Answer:

The current flowing through a wire changes with time as I=3+2t. Then, what will be the electric charge flowing through any cross section of the wire at t=4 seconds?

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Current is the rate that charges flow through a wire. Since we have an equation for the current as a function of time, it represents the instantaneous current.

You can easily calculate the current at any moment in time (as many others have already answered). If you needed the current at a time of 4 seconds, then it would be I = 3 + 2(4) = 11 Amps

If you are looking for charge, it is more complicated. As pointed out by already by Peter Upton, the charge flowing through a wire is measured over a span of time and not at a single moment in time. If you know the start and end times, then you can calculate the amount of charge, but it is based on calculus, integrating over the time span. Graphically, it is the area under the curve of current with respect to time. For your particular equation if you need to find the total charge that has gone through the wire from 0 s to 4 s, it would be:

q = (3(4) + (4)^2) - (3(0) + 4(0)^2) = 28 Coulombs