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.
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.41P
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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 = ec + R1 Iin(t)
***This is an example from my dynamics book and not a homework problem.
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