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I have a question from which I want to understand how to decipher what method of solution should I use ...
Q. The current throigh a wire depends on time as
i = io + At where i0 = 10 Amp. and A = 4 Amp/sec.
Find the charge crossed through a section of the wire in 10 secs.
it is a quite easy question.
The only thing that you have to keep in mind is that current is flow of charge particles i.e. charges flow per unit of time is called current.
therefore, i = dQ/dt , where Q is the charge flow across the wire
so the equation can be written as
dQ/dt = i0 + At
dQ = ( i0 + At ) dt
integrating both sides we get,
Q = ( i0 + At/2)*t + C0
now, when t = 0, Q= 0,
therefore, C0 = 0
thus at t = 10,
Q = 300 C
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