# First-order circuit

Discussion in 'Homework Help' started by ihaveaquestion, May 8, 2009.

1. ### ihaveaquestion Thread Starter Active Member

May 1, 2009
314
0
http://img508.imageshack.us/img508/2504/1234567.jpg

Problem states:
Find and sketch the zero state response for t > 0 in the circuit.
iS is a 10-mA step at t = 0.

I can solve this problem trivially basically based off the first paragraph I wrote at the top explaining what happens as time passes, but my teacher for some reason cares about writing the differential equations etc

I think I wrote this solution from her.

The VI relationship for the inductor is V = Ldi/dt

The part I'm concerned about is the fact that while say the current across the resistor is V/R, which I'm fine with, there is a substitution there for V for the relation stated about (Ldi/dit) giving iR = (Ldi/dt)/R forthe first order differential equation.

How can we substitute the VI relationship for an inductor when we're talking about a resistor?

2. ### steveb Senior Member

Jul 3, 2008
2,433
469
That is a result of the fact that the resistor and inductor are in parallel with the same voltage across both.

May 1, 2009
314
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Ahh I see..

May 1, 2009
314
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5. ### steinar96 Active Member

Apr 18, 2009
239
4
Are you sure this is not sequential switching, that is it's closed until t = 0. Then it opens for 1 second and then closes again.

When i was solving these problems you were supposed to assume the switch had been in it's drawed position from -infinity to the time it switched. If thats the case the initial voltage across it is zero. And when the switch closes you should have a differential equation with a forced response. Meaning you'll solve for the natural response and a particular integral which you add together for the total response.

Then you'd have to find the values of Vc at t = 1 and use those to solve for time t>1 when the forcing function (the voltage source) has been cut off from the circuit. The differential equation for that time should just be the natural response solved with the initial conditions for t = 1.

If this is sequential switching then this is the way to go.

6. ### ihaveaquestion Thread Starter Active Member

May 1, 2009
314
0
Sorry I forgot to update, what I have is the right answer.