3.3 Electrical Systems 37 Finally, we can solve Eq. (3.49) for current 1₂ and substitute the result into Eq. (3.45) to obtain the dynamic equation for the capacitor Céc =lin(1). Multiplying Eq. (3.50) by R₁ + R₂ and rearranging yields ec Rilin(t) R₁ + R₂ R₁ + R₂ (3.50) (R₁ +R₂) Céc+ ec = R₂lin(t) (3.51) Equation (3.51) is the mathematical modeling equation for the electrical system. The system is a linear first-order ODE as the circuit consists of a single capacitor. The reader should note that all terms in Eq. (3.51) are voltages.

3.3 Electrical Systems 37 Finally, we can solve Eq. (3.49) for current 1₂ and substitute the result into Eq. (3.45) to obtain the dynamic equation for the capacitor Céc =lin(1). Multiplying Eq. (3.50) by R₁ + R₂ and rearranging yields ec Rilin(t) R₁ + R₂ R₁ + R₂ (3.50) (R₁ +R₂) Céc+ ec = R₂lin(t) (3.51) Equation (3.51) is the mathematical modeling equation for the electrical system. The system is a linear first-order ODE as the circuit consists of a single capacitor. The reader should note that all terms in Eq. (3.51) are voltages.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Can I please get assistance with the transition from equation (3.49) through equation (3.51)? Step by Step

Equation (3.49) is as follows.

(R₁+R₂) I₂ = e_c + R₁ I_in(t)

***This is an example from my dynamics book and not a homework problem.

3.3 Electrical Systems 37
Finally, we can solve Eq. (3.49) for current 1₂ and substitute the result into Eq. (3.45) to obtain the dynamic equation for the
capacitor
Céc =lin(1).
Multiplying Eq. (3.50) by R₁ + R₂ and rearranging yields
ec
Rilin(t)
R₁ + R₂ R₁ + R₂
(3.50)
(R₁ +R₂) Céc+ ec = R₂lin(t)
(3.51)
Equation (3.51) is the mathematical modeling equation for the electrical system. The system is a linear first-order ODE as
the circuit consists of a single capacitor. The reader should note that all terms in Eq. (3.51) are voltages.

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