P 2.2-1 An element has voltage v and current i as shown in Figure P 2.2-1a. Values of the current i and corresponding voltage v have been tabulated as shown in Figure P 2.2-1b. Determine if the element is linear.

Figure P 2.2-1

An electrical element is linear if it satisfies both superposition and homogeneity.

Superposition requires that a model that produces a v from an i, then consider two such points that follow:

Homogeneity requires that a model that produces a v from an i, then consider the following:

Choose two points, let’s use (v,i) (12, 2) and (32,4) I choose this to make the homogeneity condition easier since 2(2) is 4, so we can make k = 2.

Superposition

However, we have the point(60, 6) so is not

So Superposition fails.

Homogeneity

But 4 should have gone to 24 since k would be 2. So Homogeneity fails also.

Finally, using MATLAB we can plot these points and see clearly the function is not linear.

Clearly this plot is not linear!

%Program to Plot Element Properties in Problem 2.2-1 to determine

%if the element is a linear element.

%Version 2018-12-27 D.W. Donovan

clear all;

v = [-3 -4 0 12 32 60]';

i = [-3 -2 0 2 4 6]';

x = i;

y = v;

figure

hold on

plot(i, v, 'k *','MarkerSize',12)

tt1 = 'PH 320 Homework Problem 2.2-1';

tt2 = 'Voltage vs Current for a Circuit Element';

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

tnl = '\newline';

ttf = [tt1 tnl tt2 tnl ttn date];

xl = 'Current, i, (A)';

yl = 'Voltage, v, (V)';

sp = 1;

axxmin = min(x)-sp;

axxmax = max(x) + sp;

axymin = min(y) - sp;

axymax = max(y) + sp;

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 27, 2018