# voltage in RC/RL circuits - simple problem

Discussion in 'Homework Help' started by studentofcomputerscience, Oct 21, 2009.

1. ### studentofcomputerscience Thread Starter New Member

Oct 21, 2009
6
0
Hello!

I've got two exercises:
1. Draw every time function (voltage across any element and current in any circuit element) which might possibly appear in first-order circuit i.e. in a circuit with one and only one capacitor or inductor and an undefined number (possibly large) of resistors and constant sources (both voltage and current) switched at t=0.
2. Assume a simple serial RL circuit with a real inductor (i.e. with internal resistance R_L). How can you calculate R_L from the voltage U_L(t)? Give appropriate expression.

It is my solution:
http://i34.tinypic.com/2lwohef.jpg
However, I don't know how to sketch graph of Uc (first exercise) and calculate internal resistance of coil (second exercise). How to take into account many sources (especially I don't know what to do with ideal current sources) or resistors (first exercise)? Can you help me, please?

Greetings!

2. ### studentofcomputerscience Thread Starter New Member

Oct 21, 2009
6
0
Hello! I don't understand why there are no answers. I presented my attempt to solution and I guess it is rather simple problem. Of course I know nobody is obliged to answer my question, however I don't know how to solve these two problems correctly (I only noticed one error in my solution - i.e. in first exercise for t=infinity, value of U_c is not zero). Greetings!

3. ### hgmjr Moderator

Jan 28, 2005
9,030
215
Be aware that many members who are able to help you are not on the forum at this time. Usually you will get a reply in several hours but sometimes it takes the better part of a day for a member to notice your post among all of the others in the forum and take the time to develop an answer.

hgmjr

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
784
In response to the first question:

There are really only two basic forms for a first order response - whether it's for a voltage or a current.

If the effective circuit time constant is T, then the two types of expression for a voltage response across any ideal element (R, L or C) driven by constant current or voltage sources would be either

V(t)=Vm*(1-exp(-t/T))

or

V(t)=Vm*exp(-t/T)

where Vm is the maximum value. Similar forms for current response would apply.

In response to the second:

If the only goal is to find the resistive component of the inductance then you would simply consider the circuit when it reaches steady state condition (notionally at t=∞)

Under this condition the only voltage drops would be in the main series resistor and the inductor's resistance. So if the circuit were driven by a constant voltage source E then the value of R_L would be found from the relationship

U_L(∞)=E*RL/(R+RL)

So if E=10V, R=100Ω and U_L(∞)=1V

Solve the relationship 1=10*RL(100+RL) to find the unknown RL (100/9=11.11Ω)

Hope this helps.