# Homework Help: Natural and free response

1. Jun 14, 2010

### 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.

#### Attached Files:

• ###### Circuit.jpg
File size:
3.6 KB
Views:
103
2. Jun 14, 2010

### 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.

3. Jun 14, 2010

### dhruv.tara

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.

4. Jun 14, 2010

### 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.

5. Jun 15, 2010

### 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.)