Problem with series RLC circuit and dependent source

[e0ne199]

Homework Statement

here is my problem :

Homework Equations

like usual, the problem is related with RLC circuits and transients

The Attempt at a Solution

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from here, the solution is obviously wrong because from the solution, its alpha should be -300 and not -0.4...and from the question it implies that i have to use 1st order differential equation while RLC equations i know use 2nd order differential equations..do you know how to solve this?? thanks before

 

[NascentOxygen]

The circuit current is the current in the dependent source. The current in the dependent source is proportional to the voltage on the capacitor plates (so this current is not going to be constant).

Inductor current I_L is just circuit current, perhaps with a "–" sign prepended.

 

[e0ne199]

The circuit current is the current in the dependent source. The current in the dependent source is proportional to the voltage on the capacitor plates (so this current is not going to be constant).

Inductor current I_L is just circuit current with a "–" sign prepended.

i know that much but would you like to explain how to arrive to the answer? because that is the one troubling me the most (the answer is on the question i posted above)

 

[vela]

Because of the dependent source, this isn't a typical RLC circuit, so you can't just plug numbers into formulas that aren't valid for this situation.

The hint pretty much tells you what you need to do. Derive a differential equation for the circuit.

 

[e0ne199]

Because of the dependent source, this isn't a typical RLC circuit, so you can't just plug numbers into formulas that aren't valid for this situation.

The hint pretty much tells you what you need to do. Derive a differential equation for the circuit.

yes i know about it but could you give me some clue about it? because it is first order DE that the solution needs not second order DE...

 

[NascentOxygen]

What is the differential equation relating a capacitor’s current to capacitor voltage?

 

[e0ne199]

I=C*dv/dt...then?

 

[NascentOxygen]

For the given circuit, you are told i = –3•v_c
so make this substitution for i in your differential equation, then solve.

 

[e0ne199]

For the given circuit, you are told i = –3•v_c, so make this substitution for i in your differential equation, then solve.

ok i see that -3Vc=C*dV/dt but what i don't understand is its differential equation...hmm do you mean the differential equation is C*dV/dt+3Vc=0? and also i don't see I_L involved there..

 

[NascentOxygen]

ok i see that -3Vc=C*dV/dt but what i don't understand is its differential equation...hmm do you mean the differential equation is C*dV/dt+3Vc=0?

Yes, solve for V_c in C*dV_c/dt + 3V_c = 0

 

[e0ne199]

Yes, solve for V_c in C*dV_c/dt + 3V_c = 0

hmmm btw would you like to explain about why it doesn't involve inductor and resistor in the differential equation? i still don't really understand since the circuit involves R, L, and C..

 

[NascentOxygen]

The current source is an active circuit, built of ICs and transistors, and you are told how it sets the circuit current. The inductor plays no part in setting current, as your equation shows. Of course, the inductor plays its rôle in determining the voltage across itself and hence the voltage on one side of the capacitor.

A dependent current source varies its voltage over whatever range is necessary in order to make the current through it obey the required relation.

 

[e0ne199]

The current source is an active circuit, built of ICs and transistors, and you are told how it sets the circuit current. The inductor plays no part in setting current, as your equation shows. Of course, the inductor plays its rôle in determining the voltage across itself and hence the voltage on one side of the capacitor.

A dependent current source varies its voltage over whatever range is necessary in order to make the current through it obey the required relation.

ok i understand..but after i have solved Vc how does it relate to I_L(t)?because the answer is I_L(t)=30e^-300tA..(From the question Vc (0^-) is 10V, so probably when t=0⁺ Vc=10V)

 

[NascentOxygen]

Once you have the equation for v_c(t) you triple it and give it a "–" sign and call it i(t) as shown by their relationship in post #8.

The problem statement specifies the initial conditions, viz., v_c(0) = 10 volts