RCL series circuit analysis: Damping Constant

[hoangpham4696]

Homework Statement

Please help me to confirm if my approach is correct. If not, please guide me to a right approach. Thank you

Relevant Equations

$$ \zeta=\frac{R}{2}(\sqrt{\frac{C}{L}})$$

$$v(c)=A_{1}exp(\frac{-t}{\tau_{1}})+A_{2}exp(\frac{-t}{\tau_{2}})+A_{3}$$

I am trying to find a damping constant of this circuit and below is my analysis. I just want to confirm if my approach is correct.

At t > infiniti, the switch will be closed. Therefore, Req for damping constant equation will just be Rx because R2 because R2 is neither in series or parallel with R1. As per calculation, damping constant is equal to:

$$\zeta=\frac{R}{2}(\sqrt{\frac{C}{L}})=\frac{3}{2}(\sqrt{\frac{6.8nF}{9.1mH}})=1.296$$

In this case, the equation for critical damping RCL circuit will be:

$$v(c)=A_{1}exp(\frac{-t}{\tau_{1}})+A_{2}exp(\frac{-t}{\tau_{2}})+A_{3}$$

Switch is close when t> Infiniti. Therefore, $A_{3}$ will be 0.

Please help to confirm if my approach is correct. Thank you so much.

 

[BvU]

Homework Statement: Please help me to confirm if my approach is correct.

Can you please post the complete, verbatim problem statement ?

$$v(c)=A_{1}\exp(\frac{-t}{\tau_{1}})+A_{2}\exp(\frac{-t}{\tau_{2}})+A_{3} \tag{1}$$

Where did you get (1) ?

At t > infiniti, the switch will be closed. Therefore, Req for damping constant equation will just be Rx because R2 because R2 is neither in series or parallel with R1. As per calculation, damping constant is equal to:

$$\zeta=\frac{R}{2}(\sqrt{\frac{C}{L}})=\frac{3}{2}(\sqrt{\frac{6.8nF}{9.1mH}})=1.296$$

In this case, the equation for critical damping RCL circuit will be:

$$v(c)=A_{1}\exp(\frac{-t}{\tau_{1}})+A_{2}\exp(\frac{-t}{\tau_{2}})+A_{3}$$

Switch is close when t> Infiniti. Therefore, $A_{3}$ will be 0.

1. What do you mean with t> Infiniti

2. there is no Rx anywhere in sight. Do you mean R1 ?

3. Did you notice I1 is a current source ?

4. 'this case'? Where does the 'critical damping come from ? Does (1) apply to that case ?

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