How to Determine Relay Operation Cycle Time Using Natural and Forced Response?

[dhruv.tara]

I have this circuit that I have attached with the question, Its given that V=100 V, R1= 30, R2= 70 and R3 = 3. L = 1/11 H

The switch in the circuit represents a current operated relay, the contact of which close when current through inductor is 0.9 A and opens again when current is 0.25 A through the inductor. I am supposed to find the time period for one cycle of relay operation.

I could get the answer from the traditional method. Taking the first open circuit in account I found i(t) and got when the circuit will be closed for the first time. Then solving the first order differential equation for the closed circuit found when the circuit will be open again. And I got the answer.

Now I wanted to approach the same problem using i = i natural + i forced. But got wrong answer, (rather no answer) using this approach. I am new to the formula so trying to get used to it. Any help is appreciated.

 

[Phrak]

You haven't specified initial conditions. Pick the easy solution that obtains when the coil initially has greater than 0.9 amps, and Bob's your uncle.

 

[dhruv.tara]

You haven't specified initial conditions. Pick the easy solution that obtains when the coil initially has greater than 0.9 amps, and Bob's your uncle.

hmm initially there is no energy in the inductor. And I want a way to use the i = in + if form to get my answer.

 

[Phrak]

I'm not sure what you're up to. There is no second order part--no sinusoidal components in the current or voltage. For this to happen you would need some capacitance somewhere. All your variables in V and I will be first order.

 

[Antiphon]

He doesn't need a capacitor. It's a non-linear relaxation oscillator. (peicewise linear to be precise which is how he needs to analyze it.)