Electrical circuits can usually be considered as an interconnection of lumped elements. FIGURE Q1 shows a R-L-C circuit where V, is the input voltage source and V, is the output voltage. R1 L R2V FIGURE Q1 The equations based on electrical laws are the following: V2 - ig R. Vz. =ig R, diz i, =cac, v, - L- dt dt i=i, = 1g, , V½, =Vc =V, V =V½ +V½+V¢• i=ic, +Í2, Note that the currents and voltages through the elements (capacitor, inductor and resistor) are expressed through the appropriate subscripts. a. Solve a state space representation using the following variables as states: [VR3İR:].

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1.
Electrical circuits can usually be considered as an interconnection of lumped
elements. FIGURE Q1 shows a R-L-C circuit where V, is the input voltage source
and V, is the output voltage.
R1
L
V,
C
R2 Vo
FIGURE Q1
The equations based on electrical laws are the following:
Vz = i, R, VR, =iz R
diz
V =L
dt
=
dt
i=iz = ig , Va, =Vc =V,
V; =V +V½ +V¢, i =ic, +ÎR,
Note that the currents and voltages through the elements (capacitor, inductor and
resistor) are expressed through the appropriate subscripts.
a.
Solve a state space representation using the following variables as states:
[VR1İR:].
Transcribed Image Text:1. Electrical circuits can usually be considered as an interconnection of lumped elements. FIGURE Q1 shows a R-L-C circuit where V, is the input voltage source and V, is the output voltage. R1 L V, C R2 Vo FIGURE Q1 The equations based on electrical laws are the following: Vz = i, R, VR, =iz R diz V =L dt = dt i=iz = ig , Va, =Vc =V, V; =V +V½ +V¢, i =ic, +ÎR, Note that the currents and voltages through the elements (capacitor, inductor and resistor) are expressed through the appropriate subscripts. a. Solve a state space representation using the following variables as states: [VR1İR:].
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