The voltage pulse applied to the 100 mH inductor shown in Fig. 6.5 is 0 for $t\lt 0$ and is given by the
expression
$v\left(t\right) = 20te^{-10t} V$
for $t \gt 0$ . Also assume i=0 for $t \leq 0$

a) Sketch the voltage as a function of time.

b) Find the inductor current as a function of time.

c) Sketch the current as a function of time.

Question

The voltage pulse applied to the 100 mH inductor shown in Fig. 6.5 is 0 for [latex]t\lt 0[/latex] and is given by the
expression

[latex] v\left(t\right) = 20te^{-10t} V [/latex]

for [latex]t \gt 0 [/latex]. Also assume i=0 for [latex]t \leq 0 [/latex]

a) Sketch the voltage as a function of time.

b) Find the inductor current as a function of time.

c) Sketch the current as a function of time.

Accepted Answer

a) The voltage as a function of time is shown in Fig. 6.6.

b) The current in the inductor is 0 at t=0 . Therefore, the current for t>0 is

[latex]i=\frac{1}{0.1} \int_{0}^{t}{20 au e^{-10 au }d au }+0[/latex]

[latex]=200\left[\frac{-e^{-10 au }}{100} \left(10 au +1 ight) ight]\mid ^{t}_{0}[/latex],

[latex]=2\left(1-10te^{-10t }-e^{-10t } ight) A, t\gt 0 [/latex].

c) Figure 6.7 shows the current as a function of time.

Question 6.2: The voltage pulse applied to the 100 mH inductor shown in Fi...