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

The fundamental frequency , The frequency domain representation of a signal...

The frequency domain representation of a signal is shown  below: i. What are the fundamental frequency and the corresponding period of this signal (shown in Figure )? ii.  Pl

Find the frequency at which the forced response is zero, Q. The response y(...

Q. The response y(t) of a linear system to a unit-step excitation is y(t) = (4 - 10e -t + 8e -2t )u(t). (a) Find the system function. (b) Find the frequency at which the fo

Explain contact resistance, Explain Contact resistance. Contact resista...

Explain Contact resistance. Contact resistance: It is measured as the voltage drop from tail to tail of the mated contacts along with specified current flowing through the cont

Find vout in the circuit, (a) Find v out in the circuit shown in Figure. ...

(a) Find v out in the circuit shown in Figure. (b) With V i = 2V, R 1 = R 2 = 2.5k, R 3 = 5k, and A = 100, find v out .

How many simultaneous calls can be made during peak time, Q. In a hundred-...

Q. In a hundred-line exchange 24 two-motion selectors are used. Draw schematic you suggest for this exchange and illustrate its working. How many simultaneous calls can be made du

Explain polling, What is meant by polling? In polling schemes, a set of...

What is meant by polling? In polling schemes, a set of address lines is driven by the controller to address every of the masters in sequence. When a bus request is received fro

Role of bureau of energy efficiency, Role of Bureau of Energy Efficiency ...

Role of Bureau of Energy Efficiency The role of the Bureau of Energy Efficiency is to: Ready standards and labels of appliances and equipment; Develop a list

Find the fourier transform of the signal, Problem (a) Give an example...

Problem (a) Give an example of a power signal and one example of an energy signal. (b) Given a periodic signal x (t) = A sin (2Bft). Calculate the power Px. (c) Diffe

Determine overall power factor of the combined load, Q. Two balanced, three...

Q. Two balanced, three-phase, wye-connected loads are in parallel across a balanced, three-phase supply. Load 1 draws 15 kVA at 0.8 power factor lagging, and load 2 draws 20 kVA at

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