The independent current source in the circuit shown in Fig. 6.2 generates zero current for t

Question

The independent current source in the circuit shown in Fig. 6.2 generates zero current for [latex] t\lt 0 [/latex]and a pulse [latex]10te^{-5t} A[/latex],for [latex]t\gt 0 [/latex].
a) Sketch the current waveform.
b) At what instant of time is the current maximum?
c) Express the voltage across the terminals of the 100 mH inductor as a function of time.
d) Sketch the voltage waveform.
e) Are the voltage and the current at a maximum at the same time?
f) At what instant of time does the voltage change polarity?
g) Is there ever an instantaneous change in voltage across the inductor? If so, at what time?

Accepted Answer

a) Figure 6.3 shows the current waveform.

b)[latex]\frac{di}{dt} =10\left(-5 t e^{-5t}+e^{-5t}\right)=10e^{-5t} \left(1-5t\right) \frac{A}{s}[/latex] ; [latex]\frac{di}{dt}=0 [/latex] when [latex]t=\frac{1}{5}s[/latex].(See Fig. 6.3.)

c)[latex]v=\frac{Ldi}{dt} =\left(0.1\right) 10e^{-5t}\left(1-5t\right)=e^{-5t} \left(1-5t\right) V,t>0;v=0, t\lt 0[/latex].

d) Figure 6.4 shows the voltage waveform.

e) No; the voltage is proportional to [latex]\frac{di}{dt} [/latex] , not i.

f) At 0.2 s, which corresponds to the moment when [latex]\frac{di}{dt} [/latex] is passing through zero and changing sign.

g) Yes, at t=0 . Note that the voltage can change instantaneously across the terminals of an inductor.

Question 6.1: The independent current source in the circuit shown in Fig. ...

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