# v(t) and i(t) plots for coil and capacitor

Discussion in 'Homework Help' started by studentofcomputerscience, Oct 28, 2009.

1. ### studentofcomputerscience Thread Starter New Member

Oct 21, 2009
6
0
Hello !

I'd like to plot the curves of voltage and current dependent on time for the circuit with coil and capacitor. However, I've got some difficulties with applying physical method, i.e. substituting coil and capacitor for the proper short circuit / open circuit / voltage source / current source.

The exercise is as follows: Draw all possible waveforms of
a) a current i(t) and voltage u(t) in the second-order circuit shown in Fig. 1
b) a current i(t) in the third-order circuit shown in Fig. 2
c) a current i(t) in the fourth-order circuit shown in Fig. 3
I begin with (a), the figure contains source e_g(t) with R_g, there are also Rd, R, R, C, L, R_L. It is shown here: http://i34.tinypic.com/ivic5x.jpg

My attempt to solving this problem is here: http://i37.tinypic.com/j9xc1e.jpg
(And the other exercises from this set are here: http://i38.tinypic.com/n3rjbo.jpg).

Can you help me to solve it, please?
Greetings !

2. ### studentofcomputerscience Thread Starter New Member

Oct 21, 2009
6
0
Can anybody help me with solving it, please? This time, hgmjr, I posted it at the time when "many members who are able to help me are present on the forum" .

3. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
Forums members are probably reluctant to reply because the question (a) alone is (unnecessarily) complicated with all those variable resistors.

At its most basic, a second order network has three possible responses - viz. over-damped, critically damped or under-damped.

As no values other than Rg=600Ω are given, one would just assume both responses i(t) or u(t) fall into one of the three possibilities and draw a general time response.

Assumptions I would make (for simplicity) in a basic approach:
1. The source Eg(t) is a single pulse of sufficient duration that the individual values i(t) and u(t) have reached steady state in response to the low-to-high transition before the high-to-low transition occurs.
2.Say Eg(t)=E when high.
3.Set Rd to achieve the desired damping condition and R(variable) to zero.

Now with E(t) high.....
For the case of i(t), the final value will then be given by E/(Rg+RL+R+Rd). The initial value of i(t) will be E/(Rg+R+Rd).

So for the over-damped and critically damped cases, i(t) starts at E/(Rg+R+Rd) and falls asymptotically to E/(Rg+RL+R+Rd). The fall to steady state is quickest at critically damping.
For the under-damped case, the response would see i(t) start at E/(Rg+R+Rd), and then exhibit an exponentially decaying oscillation (with some undershoot) about the final value E/(Rg+RL+R+Rd). The length of the oscillation depends on the degree of damping - getting longer as damping reduces.

So that's just one situation - considering all the others would become too painful for my liking.

Whoever sets these problems is very "mean spirited".