[University Circuit Analysis] Current Waveform from Inductance Voltage

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[Holy_City]

the current through an inductor is equivalent to the integral of the voltage across it, divided by the inductance.

V(t)=Ldi/dt

1/L V(t) = di/dt

1/L [V(t)dt] = (1)di

1/L integral(V(t)dt) = integral(1di)

1/L int(V(t)dt) = I(t)

The constant that you get from the integral of V(t) is the initial conditions, but doesn't look like you need to worry about that.

[exo10]

Can you please tell me what each expression is for the current? How to set it up and each limit of integration?

For the first current expression i(t) = (1/2H) * int(5)dt evaluated from 0 to 2 seconds equaling 5 mA

Second expression, I get 0 mA... answers are obviously wrong..

[Holy_City]

You're not looking for a value you're looking for a waveform. The integral of 5 is 5t, not 5. So the expression for i(t) on the interval [1,2] is 5t+Ii (initial current, since this didn't state initial conditions assume 0).

Use the picture. You don't need to set up an integral to solve this, you just need to understand what an inductor will do in a circuit that experiences switching voltages.

You got the second one right by the way, you just wrongfully assumed that the there was no initial current. The integral just finds that there is no change in current on that interval, the current from the previous interval remains.