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Partial circuit shown in attachment. A current pulse is fed to the partial circuit shown in Figure P32.25. the current begins at zero, then becomes 10.0A between t = 0 and t = 200 microseconds, and then is zero once again. Determine the current in the inductor as a function of time. I1 is the current before the junction, I2 is the current through the resistor, I3 is the current through the inductor, and R is the 100 Ohm resistance.
The current is 0A when t < 0s. For t between 0 and 200 microseconds, I used Kirchoff's Method and came up with:
L*dI3/dt = (I1  I3)*R...from here on I came up with a differential equation and got:
I3 = 10(1  e^(10000t), which is the answer I'm supposed to get, although when coming up this, I had to assume I1 was unaffected by the inductance and remained as 10A through the time interval.
Where I am stuck at is finding the current when t > 200 microseconds. The answer I'm supposed to get is I3 = (63.9A)*e^(10000t), in which 63.9A is the initial current right after the current pulse is gone. I can get the format of the equation, but I just dont know how to find that the initial current is 63.9A...help?
The current is 0A when t < 0s. For t between 0 and 200 microseconds, I used Kirchoff's Method and came up with:
L*dI3/dt = (I1  I3)*R...from here on I came up with a differential equation and got:
I3 = 10(1  e^(10000t), which is the answer I'm supposed to get, although when coming up this, I had to assume I1 was unaffected by the inductance and remained as 10A through the time interval.
Where I am stuck at is finding the current when t > 200 microseconds. The answer I'm supposed to get is I3 = (63.9A)*e^(10000t), in which 63.9A is the initial current right after the current pulse is gone. I can get the format of the equation, but I just dont know how to find that the initial current is 63.9A...help?
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