An electric circuit is described by the following equation: d’u du +k+o°u= au, dt di? where t is time in seconds, and w, k, and a are positive constant parameters. a) Assuming that u is the voltage in Volts, find the physical dimensions of the constants k, w, and a in the SI system using the rule of dimension homogeneity. b) Present this equation in the form of the energy balance equation. Find the total instantaneous energy of the circuit E and the dissipative function F.

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An electric circuit is described by the following equation:
d’u
du
+k+o°u= au,
dt
di?
where t is time in seconds, and w, k, and a are positive constant parameters.
a)
Assuming that u is the voltage in Volts, find the physical dimensions of the
constants k, w, and a in the SI system using the rule of dimension homogeneity.
b)
Present this equation in the form of the energy balance equation. Find the total
instantaneous energy of the circuit E and the dissipative function F.
Transcribed Image Text:An electric circuit is described by the following equation: d’u du +k+o°u= au, dt di? where t is time in seconds, and w, k, and a are positive constant parameters. a) Assuming that u is the voltage in Volts, find the physical dimensions of the constants k, w, and a in the SI system using the rule of dimension homogeneity. b) Present this equation in the form of the energy balance equation. Find the total instantaneous energy of the circuit E and the dissipative function F.
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