# RLC circuit with DC

1. May 21, 2017

### Arman777

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
I used the loop rule where $ΣΔV=0$ and junction rule.
From here I get 4 equations
$i_3=i_1+i_2$
$ε-i_3R_3-i_1R_1-L(di\dt)=0$
$ε-i_3R_3-i_2R_2-Q\C=0$
$i_1R_1-L(di\dt)+Q\C+i_2R_2=0$

1-I said Q\C will dissapear since Q=0 at t=0. But what about (di\dt) ? Is (di\dt)=0 ? I think it should be, but If its zero I didnt understand why it asked again since we need to claim its zero to solve the question.If its not zero then I couldnt solve the upper 4 equations.İts like something is missing.

2. May 21, 2017

### cnh1995

You do not need any equations here.
Just apply what you know about the behaviour of L and C at the moment of energization i.e. t=0.

What is the current through the inductor "just before" the switch is closed?

3. May 21, 2017

### Arman777

Isnt it a time depented value ? Function like I(t)=Awcos(wt)+Bwsin(wt) ? I dont know...

4. May 21, 2017

### cnh1995

Yes.
But you only need to know what happens at t=0.

5. May 21, 2017

### Arman777

Can you help a bit more..I couldnt see the solution

6. May 21, 2017

### cnh1995

There was no source in the circuit before the switch is closed.
So what can you say about the inductor current "before" the switch is closed?

7. May 21, 2017

### Arman777

Zero ?

8. May 21, 2017

### cnh1995

Yes. So what is the inductor current just after closing the switch?

9. May 21, 2017

### Arman777

zero ?

10. May 21, 2017

### cnh1995

Yes.

11. May 21, 2017

### Arman777

You could have just say yes.. ? Are my equations wrong ? Cause I need to find currents.

12. May 21, 2017

### cnh1995

Only at t=0. As I said, you do not need any of the equations you've written.

What can you say about the current through the capacitor at t=0 i.e. just after the switch is closed?

13. May 21, 2017

### cnh1995

Ok. I think you do need to solve the equations for solving b and c because of presence of R1. The current through R1 is governed by both L and C values. My apologies.
But you do not need them to know i1 and i2 at t=0.

14. May 21, 2017

### Arman777

Question asks that,I need to know

15. May 21, 2017

### cnh1995

Yes. So what is the current through the capacitor at t=0?
How does a capacitor behave when energized at t=0?

16. May 21, 2017

### ehild

The fourth equation is not needed. And di/dt should be di1/dt.
So you have the system of equations
$i_3=i_1+i_2$
$ε-i_3R_3-i_1R_1-L(di_1/dt)=0$
$ε-i_3R_3-i_2R_2-Q/C=0$
Substitute $i_3=i_1+i_2$ for i3. You might need the relation between Q and i2. Then you have a system of equations for two currents and their derivatives.

Last edited: May 22, 2017
17. May 22, 2017

### Arman777

Zero ? At the begining there should be no current ? Seems wrong but also makes sense.
I see well I find $-i_2R_2=Q\C$ but in any case at t=0,Q=0

18. May 22, 2017

### BvU

Yes but for t>0 you should get something else

19. May 22, 2017

### Arman777

Rest of the question.Well at $t=∞$ there would be no current on the capacitor brench.

In the brench where inductor exist, there would be current.I can write an equation like, $ε-iR_3-iR_1-L(di\dt)=0$.Do I need to solve this ? I couldnt directly see the answer.
For (e) probably its $εC$.
For (f), I need to find that current passes through inductor,I know the equations and ıf my answer to e is true then I can find it easily.

20. May 22, 2017

### ehild

No, it is not true . You ignored i3, and it is not zero at t=0.