What do you mean by superposition and linearity, Electrical Engineering

Assignment Help:

Q. What do you mean by Superposition and linearity?

Mathematically a function is said to be linear if it satisfies two properties: homogeneity (proportionality or scaling) and additivity (superposition),

f (Kx) = Kf (x) (homogeneity)

where K is a scalar constant, and

f (x1 + x2) = f (x1) + f (x2) (additivity)

Linearity requires both additivity and homogeneity. For a linear circuit or system in which excitations x1 and x2 produce responses y1 and y2, respectively, the application of K1x1 and K2x2 together (i.e., K1x1 + K2x2) results in a response of (K1y1 + K2y2), where K1 and K2 are constants. With the cause-and-effect relation between the excitation and the response, all linear systems satisfy the principle of superposition. A circuit consisting of independent sources, linear dependent sources, and linear elements is said to be a linear circuit. Note that a resistive element is linear. Capacitors and inductors are also circuit elements that have a linear input-output relationship provided that their initial stored energy is zero. Nonzero initial conditions are to be treated as independent sources.


Related Discussions:- What do you mean by superposition and linearity

Determine the stresses set up in the cylinder and steel wire, A copper cyli...

A copper cylinder 40 cm diameter and 10 mm thick is nearly wound with a layer of 4mm diameter steel wire under a tensile stress of 80 Mpa. If the steam under a pressure of 5 Mpa is

Illustrate the basic working of modem, Q. Illustrate the basic working of M...

Q. Illustrate the basic working of Modem? Modem: Modems are generally provided by network operators or by vendors who aren't necessarily the manufacturers of computer systems.

Current ratio, Current ratio The ratio is mainly used to give an idea ...

Current ratio The ratio is mainly used to give an idea of the company's ability to pay back its short-term liabilities with its short-term assets. The higher the current ratio

Determine the low-pass filter and amplitude spectra, Q. Let a square-wave v...

Q. Let a square-wave voltage source having an amplitude of 5V, a frequency of 1 kHz, a pulse width of 0.5 ms, and an internal source resistance of 50  be applied to a resistive lo

Combinational-sequential, Design combinational-sequential electronic logic ...

Design combinational-sequential electronic logic gate circuit for a car wash....

Determine the 60-hz resistance of line, Q A handbook lists the 60-Hz resist...

Q A handbook lists the 60-Hz resistance at 50°C of a 900-kcmil aluminumconductor as 0.1185/mile. If four such conductors are used in parallel to form a line, determine the 60-Hz r

What is meant by wait state, What is meant by Wait State? This state is...

What is meant by Wait State? This state is used by slow peripheral devices. The peripheral devices can transmitted the data to or from the microprocessor by using READY input l

Determine the bits required for a d/a converter, Q. Determine the bits requ...

Q. Determine the bits required for a D/A converter to detect 1-V change when V ref = 15 V.

Express the storedmagnetic energy, A relay is essentially an electromechani...

A relay is essentially an electromechanical switch that opens and closes electrical contacts. A simplified relay is represented in Figure. It is required to keep the fenomagnetic p

Physics, find the resultant of two forces 20N and25N acting at an angle 60...

find the resultant of two forces 20N and25N acting at an angle 60 degree each other

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd