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Figure 1 shows an electric circuit that can be represented by a system of differential equations.

Figure 1 shows an electric circuit that can be represented by a system of differential equations.

Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter29: Dc Generators
Section: Chapter Questions
Problem 5RQ: What are interpoles, and what is their purpose?
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Question 4 Figure 1 shows an electric circuit that can be represented by a system of differential equations. Ic R2 la E R1 FIGURE 1. Electric circuit If I, and I. describe the currents of the circuit, by Kirchhoff's first law, we can write Ia (t ) = I½ (t) +Ie ().
Transcribed Image Text:Question 4 Figure 1 shows an electric circuit that can be represented by a system of differential equations. Ic R2 la E R1 FIGURE 1. Electric circuit If I, and I. describe the currents of the circuit, by Kirchhoff's first law, we can write Ia (t ) = I½ (t) +Ie ().
(a) Applying the Kirchhoff's second law, show that the system of differential equa- tions is dlb +L dt dIc L +R¡I½ = E (t), dt -R1 dlh R2 dle 1 = 0. dt Use the Laplace transform to solve the system in (a) if R1 = 102, R2 = 52, L= 1H, C= 0.2F, I,(0) = 0, Ic(0) = 0 and (b) 120, 0<t<2, E (t) = 0, t > 2. (c) Calculate the current Ia(t).
Transcribed Image Text:(a) Applying the Kirchhoff's second law, show that the system of differential equa- tions is dlb +L dt dIc L +R¡I½ = E (t), dt -R1 dlh R2 dle 1 = 0. dt Use the Laplace transform to solve the system in (a) if R1 = 102, R2 = 52, L= 1H, C= 0.2F, I,(0) = 0, Ic(0) = 0 and (b) 120, 0<t<2, E (t) = 0, t > 2. (c) Calculate the current Ia(t).
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