You are freshly employed in the design department of Tesla Motors. Your new job requires you to model battery packs that are to be installed in the upcoming Tesla Roadster. The circuit below is a simple model for modelling terminal voltage, v(t), of a battery pack. Vbatt represents the ideal DC voltage that can be provided by battery. Ro models the dissipated losses. The parallel R1 - C1 pair models, what is known as "diffusion" in batteries i.e., when a battery is allowed to rest/charge, its voltage does not immediately increases or decreases, rather builds up or decays gradually, in a capacitive fashion. i1(t) R1 ilt) RO Vbatt C1 v(t) +1

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You are freshly employed in the design department of Tesla Motors. Your new job requires
you to model battery packs that are to be installed in the upcoming Tesla Roadster. The
circuit below is a simple model for modelling terminal voltage, v(t), of a battery pack. Vbatt
represents the ideal DC voltage that can be provided by battery. Ro models the dissipated
losses.
The parallel R1 - C1 pair models, what is known as "diffusion" in batteries i.e., when a
battery is allowed to rest/charge, its voltage does not immediately increases or decreases,
rather builds up or decays gradually, in a capacitive fashion.
i:(t)
R1
ilt)
RO
Vbatt
C1
v(t)
Formulate a differential equation for i1(t) in terms of i(t) and i(t).
+1
Transcribed Image Text:You are freshly employed in the design department of Tesla Motors. Your new job requires you to model battery packs that are to be installed in the upcoming Tesla Roadster. The circuit below is a simple model for modelling terminal voltage, v(t), of a battery pack. Vbatt represents the ideal DC voltage that can be provided by battery. Ro models the dissipated losses. The parallel R1 - C1 pair models, what is known as "diffusion" in batteries i.e., when a battery is allowed to rest/charge, its voltage does not immediately increases or decreases, rather builds up or decays gradually, in a capacitive fashion. i:(t) R1 ilt) RO Vbatt C1 v(t) Formulate a differential equation for i1(t) in terms of i(t) and i(t). +1
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