Suppose the current in a conductor decreases exponentially with time according t

Question

Suppose the current in a conductor decreases exponentially with time according to the equation I(t) = I0e-t/t, where I0 is the initial current (at t = 0), and t is a constant having dimensions of time. Consider a fixed observation point within the conductor. (Use the following as necessary: I0 and t)

a) How much charge passes this point between t = 0 and t = t? (If applicable, round any coefficients to 3 decimal places.)

answers I've tried that were wrong: I_0t(1-e^-1) and I_0t(0.623) and I_0t(1-e^-01) = ALL WRONG.

Explanation / Answer

Ok. In your question you have 'e-t/t' but it should be 'e-t/T' where T is a time constant. Anyway below is the solution You know that equation for the magnitude of current passing thorough a point which is I(t) = I_0e-t/T so magnitude of charge passing through the point at time dt is dq = I_0e-t/T dt so total charge passing in the interval 0 to t is calculated by integrating the function q = I_0 (1- e^-1) = I_0 (0.632120)

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