# Simple RLC Circuit problem

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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• RLC circuit.JPG
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berkeman
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?

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

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SGT
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.
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 $$v_C$$.

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

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

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 $$V_C$$

thanks

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.

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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