P1.2-7 Find the charge q(t) and sketch its waveform when the current entering a terminal of an element is as shown in Figure P1.2-7. Assume that q(t) = 0 for t < 0.

Figure P 1.2 – 7

We know that charge can be found from

So we need to describe the curve presented in the figure

From 0 to 2 s, we have a straight line . For 2 to 4 s we have another straight line but it has a non-zero slope. Using two point form of a line we can write

Solving

Putting in the actual variables so the function for current is

i is in amperes when t is in seconds.

For

Since we are told that q(t) = 0 for t < 0

At t = 2,

For

Check for

As it should be! So q(t) can be expressed as

q is in coulombs when t is in seconds.

MATLAB Plots and Code follows:

%Program to plot out Current vs time for Homework Problem 1.2-7.

%Version 2018-12-24 DW Donovan

clear all;

ta = [-1:0.01:0]';

tb = [0:0.01:2]';

tc = [2:0.001:4]';

x = [ta' tb' tc'];

qa = 0*ta;

qb = tb;

qc = 0.5*tc.^2-tc+2;

y = [qa' qb' qc'];

tt1 = 'PH 320 Homework Problem 1.2-7';

tt2 = 'Charge vs Time for a given circuit element';

ttn = 'D.W. Donovan -- ';

tnl = '\newline';

ttf = [tt1 tnl tt2 tnl ttn date];

xl = 'Time, t, (seconds)';

yl = 'Charge, q, (C)';

sp = 1;

axxmin = min(x)-sp;

axxmax = max(x) + sp;

axymin = min(y) - sp;

axymax = max(y) + sp;

figure

hold on

plot(ta, qa,'k-','LineWidth',5)

plot(tb, qb,'k-','LineWidth',5)

plot(tc, qc,'k-','LineWidth',5)

title (ttf,'FontSize', 16)

xlabel(xl, 'FontSize', 16)

ylabel(yl, 'FontSize', 16)

axis([axxmin axxmax axymin axymax])

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This page last updated on December 24, 2018