DECE3723_Spring2018_Ho file:///C:/Users/Seth/Downloads/ECE3723,Spring2018.Homewo
ID: 2268708 • Letter: D
Question
DECE3723_Spring2018_Ho file:///C:/Users/Seth/Downloads/ECE3723,Spring2018.Homework4%20(1).pdf 1. (10 pts) Review of important concepts covered in the Lectures 8-10 of Electrical Circuits II (a) (1.25 pts) Describe the storage mechanism of an capacitor and how it is related with initial conditions? (b) (1.25 pts) Describe the storage mechanism of an inductor how it is related with initial condi- tions? (c) (1.25 pts) Define poles and zeros and explain what are the benefits of its use. (d) (1.25 pts) Define transfer function H(s) and explain what are the benefits of its use 48 PM O Type here to search ^ D dx 2/24/2018Explanation / Answer
1.
(a)
Capacitor store the energy. It is passive element. It stores the energy when the current flow throw this. It has two parallel plates opposit to each other and seperated by insulating layer. Due to this insulating layer, DC current can not flow through the capacitor. Then the voltage will be formed across the plates in the form of an electrical charge.There are two types of electrical charge, positive charge in the form of Protons and negative charge in the form of Electrons. When a DC voltage is applied across a capacitor, the positive charge quickly accumulates on one plate and opposite negative charge accumulates on the other plate. For every particle of +ve charge that arrives at one plate a charge of the same sign will depart from the -ve plate. Like this procedure voltage across capacitor will be produced. When we remove the DC source which is connected across it, then the voltage across capacitor remains change. It is called intial voltage of capacitor or intial condition.
(b)
Inductor is nothing but a wire wound or a coil. The storage capacity of inductor depends on its number of wounds. When the current flowing through this inductor then the electromagnetic flux will be produced according to the faraday's law. Due to this flux it oppose the sudden change in current. It store the energy in the form of electromagnetic flux. It has intial value as current.
(c)
"Poles" and "Zeros" of a transfer function are defined as the frequencies for which the value of the denominator and numerator of transfer function becomes zero. These are helpful to analyze whether the system is stable or not and how well the system performs. In realtime control systems we basically design a system having a number of poles greater than or equal to the number of zeros to better performance.
(d)
Transfer function ( H(s)) is defined as the ratio of laplace transform of output to the laplace transform of the input when the intial conditions are assumed to be zero. Let laplace transform of input and output is C(s) and R(s), then the transfer function H(s) is given by
H(s) = C(s)/R(s)
Benifits of transfer function.
1. Its a mathamedical model of a system and it gives the gain of the system.
2. If the transfer function of a system is known then we can easily find the response to the input very easily.
3. It is in the form of laplace trasform, So these terms are simple algebraic terms and don't have to solve differential equations.
4. Poles and zeros can be determined from this.
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