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Series RLC

198
0
1. Homework Statement
I'm having some problems solving this RLC circuit, if anyone could help.

R = 2 ohms
C = 2/3 F
L = 1/2 H

The top picture is when t < 0
The bottom picture is when t > 0
Find [tex]v_o(t)[/tex] (notice V_0 is the defined +- voltage over the resistor)
http://img503.imageshack.us/img503/448/rlcwo0.th.png [Broken]

2. Homework Equations



3. The Attempt at a Solution

Well I found that:
[tex]i_L(0^+) = 2 A[/tex]
[tex]v_c(0^+) = 0[/tex]
[tex]v_o(0^+) = -4 V [/tex]
Which I believe are correct,
I found the general equation to be [tex]v_0(t) = Ae^{-t} + Be^{-3t}[/tex]
(My main problem is finding A and B, they should be 2 and -6 but I just can't get that)

A + B = -4
[tex]dv(0^+)/dt = -A + -3B[/tex]
This is where I get a little sketchy, but since Cdv/dt = i_c then I was thinking that since [tex]i_L(0^+) = i_C(0^+)[/tex] for series circuits I could just say
[tex]-A + -3B = 2/C[/tex]
However when I solve those two equations I get A = -4.5, B = 1/2
Does anyone know what I did wrong?
 
Last edited by a moderator:

Answers and Replies

CEL
655
0
1. Homework Statement
I'm having some problems solving this RLC circuit, if anyone could help.

R = 2 ohms
C = 2/3 F
L = 1/2 H

The top picture is when t < 0
The bottom picture is when t > 0
Find [tex]v_o(t)[/tex] (notice V_0 is the defined +- voltage over the resistor)
http://img503.imageshack.us/img503/448/rlcwo0.th.png [Broken]

2. Homework Equations



3. The Attempt at a Solution

Well I found that:
[tex]i_L(0^+) = 2 A[/tex]
[tex]v_c(0^+) = 0[/tex]
[tex]v_o(0^+) = -4 V [/tex]
Which I believe are correct,
I found the general equation to be [tex]v_0(t) = Ae^{-t} + Be^{-3t}[/tex]
(My main problem is finding A and B, they should be 2 and -6 but I just can't get that)

A + B = -4
[tex]dv(0^+)/dt = -A + -3B[/tex]
This is where I get a little sketchy, but since Cdv/dt = i_c then I was thinking that since [tex]i_L(0^+) = i_C(0^+)[/tex] for series circuits I could just say
[tex]-A + -3B = 2/C[/tex]
However when I solve those two equations I get A = -4.5, B = 1/2
Does anyone know what I did wrong?
You should always solve a series circuit for [tex]v_c(t)[/tex] and a parallel circuit for [tex]i_L(t)[/tex].
Once you have [tex]v_c(t)[/tex] , you can differentiate it in order to get [tex]\frac{dv_C}{dt}[/tex]. Since the current in a series circuit is the same for all elements, you have [tex]v_c(0)[/tex] and [tex]\frac{dv_C}{dt}(0)[/tex].
Knowing [tex]v_c(t)[/tex] you can calculate [tex]v_o(t)[/tex].
 
Last edited by a moderator:

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