Engineering Circuit Analysis 10th Edition Chapter One Exercise Solutions
3 3 sin
1. We need to solve 100 1 which is a transcendental equation. Let’s solve it
3 sin
graphically. This can be done on a graphing calculator, plotting points by hand (with a
little iteration), or using MATLAB script similar to
q linspace(0, 0.5 *pi/ 2,1000);
rel_err 100 *abs(3 *q-3 *sin(q))./sin(q)/ 3;
plot(q,rel_err,'r.')
Expanding the plot and looking for a point close to 1%, we find a value of q 0.245 radians
is about the limit for the linear approximation if 1% or better accuracy is required.
, Engineering Circuit Analysis 10th Edition Chapter One Exercise Solutions
2. We start by expressing the relative error for the first function in the form
1 x
1
100 1 x 1
1
1 x
Which can be simplified to
1 x 1 x 1 0.01
1
or x 2 0.01 which has solutions x 0.1.
, Engineering Circuit Analysis 10th Edition Chapter One Exercise Solutions
V
3. We begin by rearranging VC V0 (1 e t / ) to yield t ln 1 C where VC/V0 is
V0
specified but t is not. We proceed to construct the expression for relative error, using
V V
the approximation that ln 1 C C :
V0 V0
V VC
C ln 1
Relative Error 100 0 V0
V
V
ln 1 C
V0
Mercifully, the time constant (τ) cancels in the numerator and denominator. Thus,
3
1015 atoms 102 cm
10 atoms/m it’s unclear what a “zeta atom” is
21 3
(h) 3
cm 1 m
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