# Simple RLC Circuit problem

1. Oct 16, 2006

### Raihan

Please help me to solve this RLC circuit problem. I am completely confused.If you give me the direct answer it would be much appreciated.
For the series RLC circuit in Figure, find the input/output
difference equation for

1.$$y(t)=v_{R}$$
2.$$Y(t)=i(t)$$
3.$$y(t)=v_{L}$$
4.$$y(t)=v_{C}$$

I have attached the Circuit diagram in a .jpg file.

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Last edited by a moderator: Nov 28, 2006
2. Oct 17, 2006

### Staff: Mentor

You must show your own work in order for us to help you (PF homework forum rules). Would KCL or KVL be the best way to start?

3. Oct 17, 2006

### Raihan

Hey first I tried taking the KVL around the loop
something like
$$-x(t) + v_c(t) + v_L (t) + v_R (t) = 0$$----(1)
replaced v_L(t) with first order Ldi_L(t)/dt and make an equation for
$$v_C(t)$$
and then as its in series I tried to write a function for
$$i_L(t) = \frac {v_R (t)} R$$------(2)
and for [ tex ] v_R(t)/R=C \frac {dv_c(t)} {dt} [/tex]----(3)
Then tried sub (3) in (1)
and got
$$v_C(t) = x(t) - \frac {L} {R} dv_R(t)/dt - v + R(t)$$----(4)
and then tried sub it i eqn 3. and didnt come up with a satisfactory result.
Thanks

Last edited by a moderator: Nov 28, 2006
4. Oct 18, 2006

### SGT

In series circuits you should always use $$v_C$$ as the independent variable (and $$i_L$$ in parallel circuits).
Since the current is the same for all elements, write $$v_L$$ and $$v_R$$ as functions of the current. Finally write the current as a function of $$v_C$$.

5. Oct 18, 2006

### Raihan

6. Oct 18, 2006

### SGT

Make the substitutions I suggested in your equation 1. More help will only be provided after you show some work.

7. Nov 23, 2006

### Raihan

8. Nov 23, 2006

### SGT

Post what you have done and I will give you more hints.

9. Nov 27, 2006

### Raihan

solution so far

thanks

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10. Nov 28, 2006

### SGT

In the second equation don't use the integral term. Keep it as $$V_C(t)$$.
In the two other terms replace i by $$C\frac{dV_C}{dt}$$. You get a second order equation in $$V_C$$

11. Nov 28, 2006

### Raihan

thanks

12. Nov 28, 2006

### SGT

The rules of the forum are that you must do your work. We only give hints. Rewrite the second equation with the suggestions I made and post it here.

13. Dec 6, 2006

### serienumerica

The easiest way to solve any RCL circuit with an input vs(t) is by a difference equation.

Let curr= (q1-q0)/dt

q2=2.*q1-q0 + dt**2*( -q1/(L*c) -(R/L)*curr +vs(t-dt) ).

Then everything else follows ,

Vc(t) = q2/C , VL = L * ( q2-2*q1+q0)/dt^2 , VR = R*(q2-q1)/dt
SEE http://www.geocities.com/serienumerica/RCLfree.doc

Last edited: Dec 6, 2006