Solving Series RLC Circuit Problems: Input/Output Equations & Diagram

AI Thread Summary
The discussion focuses on solving a series RLC circuit problem, specifically finding input/output difference equations for various circuit components. Participants emphasize the importance of using Kirchhoff's Voltage Law (KVL) and suggest expressing voltages and currents as functions of the capacitor voltage, v_C. One user shares their initial attempts at forming equations but struggles to derive satisfactory results. Others encourage showing work for further assistance and provide hints for rewriting equations to achieve a second-order equation in v_C. The conversation highlights the necessity of following forum rules by demonstrating progress to receive more detailed help.
Raihan
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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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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?
 
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.
Please help.
Thanks
 
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Raihan said:
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)=v_R(t)/R------(2)
and for v_R(t)/R=Cdv_c(t)/dt----(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.
Please help.
Thanks
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.
 
Thank you very much for your info SGT, would you please help little bit more.
 
Raihan said:
Thank you very much for your info SGT, would you please help little bit more.
Make the substitutions I suggested in your equation 1. More help will only be provided after you show some work.
 
I tried And I am not going anywhere. please help
 
Post what you have done and I will give you more hints.
 
solution so far

heres what I got so far.. please help after this point..
thanks
 

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  • #10
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
Would you please not mind to show me please. I have tried this so far. please help after this.
thanks
 
  • #12
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
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
 
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