P1.3-4 The charge flowing in a wire is plotted in Figure P1.3-4. Sketch the corresponding current.

 

P1_3_4

Figure P1.3-4

 

First write out the function for this plot.  Use two point forms of lines and we have four data points for the three line segments.  Using units of µs on the x axis and nC on the y axis, yields slope units of nC/µs is mA.  The four points are (0, 0), (2, 15), (4, 15), and (7,0).

 

For t < 0, q(t) =0

 

For

 

 

At t = 2

As it should!

 

For

 

 

Which is as it should be, the charge is steady at 15 nC.

 

For

 

 

Check two limits, at t = 4

At t = 7

 

These are correct.  For t > 7 q(t) = 0.  So q can be written as

 

q is in nC when t is in µs.

 

So for the three sections where q(t) is a constant, i is zero.  For the other two parts we get

 

 

And for

 

So current can be written as

 

i is in mA when t is in µs.

 

MATLAB Plots and Code follows:

 

 

%Program to plot out Current vs time for Homework Problem 1.3-4.

%Version 2018-12-24 DW Donovan

 

clear all;

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

tb = [0:0.01:2]';

tc = [2:0.001:4]';

td = [4:0.001:7]';

te = [7:0.01:8]';

x = [ta' tb' tc' td' te'];

 

ia = 0*ta;

ib = 7.5*tb./tb;

ic = 0*tc;

id = -5*td./td;

ie = 0*te;

y = [ia' ib' ic' id' ie'];

 

tt1 = 'PH 320 Homework Problem 1.3-4';

 

tt2 = 'Current vs Time for a wire';

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

tnl = '\newline';

ttf = [tt1 tnl tt2 tnl ttn date];

xl = 'Time, t, (\mus)';

yl = 'Current, i, (mA)';

 

sp = 1;

axxmin = min(x)-sp;

axxmax = max(x) + sp;

axymin = min(y) - sp;

axymax = max(y) + sp;

 

figure

hold on

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

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

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

plot(td, id,'k-','LineWidth',5)

plot(te, ie,'k-','LineWidth',5)

 

title (ttf,'FontSize', 16)

xlabel(xl, 'FontSize', 16)

ylabel(yl, 'FontSize', 16)

axis([axxmin axxmax axymin axymax])

 

 

Please send any comments or questions about this page to ddonovan@nmu.edu

This page last updated on December 24, 2018