# Series RLC Circuit & Differential Equations

• Engineering
pags920

## Homework Statement

I have a series RLC circuit, no values given, connected to a voltage source Vs(t). I am asked to write the differential equations for:

a. that relates the inductor current iL(t) to the source voltage Vs(t).
b. that relates the capactor voltage Vc(t) to the source voltage Vs(t).

## The Attempt at a Solution

I was told that all it is was the general equation for a series RLC circuit:

L(d^2/dt^2) + R(di/dt) + (1/C)i = 0

Any help would be very appreciated.

CEL

## Homework Statement

I have a series RLC circuit, no values given, connected to a voltage source Vs(t). I am asked to write the differential equations for:

a. that relates the inductor current iL(t) to the source voltage Vs(t).
b. that relates the capactor voltage Vc(t) to the source voltage Vs(t).

## The Attempt at a Solution

I was told that all it is was the general equation for a series RLC circuit:

L(d^2/dt^2) + R(di/dt) + (1/C)i = 0

Any help would be very appreciated.

## The Attempt at a Solution

If you have a series circuit, you should use KVL:

$$V_L + V_R + V_C = V_S$$
Now
$$V_L = L\frac{di}{dt}$$
$$V_R = R i$$
$$i = C \frac{dV_C}{dt}$$

Replace this in the KVL equation and you have the equation for the capacitor voltage.

Khamul
Hello! I too had to do a couple of these back in my D.E. Class!

First and foremost, a picture would be a great deal of help, secondly, depending on where your junctions are, and the amount/location of your resistors/capacitors/inductors, it's going to vary your equations.

Also, a really important thing to note is, if there ARE capacitors in your circuit, you're going to have to write every in that loop with the capacitor, in terms of charge.

There are two different ways you can do this, i'll try and make a little chart to help you out:

In terms of Current -- Use this if only inductors and resistors are present
Er(resistor)= R * i
EL(inductor)= L * di/dt
EC(capacitor)= N/A

In terms of Charge -- You must use this if you have a capacitor present, to relate everything
Er(resistor)= R * dq/dt
EL(inductor)= L * d2q/dt2
EC(capacitor)= (1/c)*q

If you have multiple branches (I cannot help unless I see a diagram) you will also have multiple equations.

But other than that, i'm still new to the site so...sorry about my lack of proper equation making skills!

queenstudy
i had to prove it and i did all the steps . I know the magnitude of the impedence of the circuit , but can anyone please do a detailed calculation by using phasors for this equation?? and thank you

Staff Emeritus