subject
Engineering, 27.11.2019 05:31 arod5702

To use the phasor transform and its inverse with sinusoidal functions. we are developing a technique for analyzing the steady-state response of a circuit whose source is sinusoidal. performing this analysis in the time domain, even for a simple circuit with a sinusoidal voltage source, a resistor, and inductor in series, results in a differential equation whose solution is difficult to calculate. as often happens in engineering problems, we can transform the problem from the time domain to a different mathematical "space," in this case the frequency domain. in the frequency domain, we can ana much easier to solve. here we introduce the method for transforming from the time domain to the frequency domain. we always start in the time domain by representing any sinusoidal functions using the cosine (not the sine) function. the phasor that corresponds to a given cosine function is a complex number that carries the amplitude and phase angle of the cosine, but not its frequency. for example, consider a circuit with a sinusoidal current source described by the following time-domain equation: i(t) = im cos(wt+0). we can perform the phasor-transform operation on this sinusoidal current to calculate the phasor current as follows:
i= p{i(t)} = p{im cos(wt + 0)} = im 20.

the phasor-transform operation takes a time-domain function described using the cosine function and represents it as a phasor, which is a complex number that in polar form has the magnitude and phase angle of the cosine function. phasors exist in the frequency domain where the frequency of the phasor is a constant and is not explicitly represented by the value of the phasor. we will use the phasor transform operation to transform a circuit with a sinusoidal source in the time domain to a circuit with a phasor source in the frequency domain. we will then use familiar circuit analysis to solve the circuit in the frequency domain; our solution will consist of phasor voltages and currents. but we ultimately want the steady-state time-domain solution, so we will need to transform the phasor voltages and currents back to the appropriate sinusoidal time-domain voltages and currents. we do this by using the inverse-phasor-transform operation on the phasor as follows:

i(t) = p-{i} = p-! {imzp} = im cos(wt +0).
note that we need to know the frequency of the time-domain source to use the inverse-phasor transform operation. that's because the phasor contains only the magnitude and phase angle of the time-domain cosine waveform, but not its frequency. part d - use phasors to find the value for a sum of sinusoids suppose you want to find the sum of two sinusoidal voltages, given as follows: vi(t) = v1 cos(wt+01) and v2 (t) = v2 cos(wt+ if you stay in the time domain, you will have to use trigonometric identities to perform the addition. but if you transform to the frequency domain, you can simply add the phasors v1 and v2 as complex numbers using your calculator. your answer will be a phasor, so you will need to inverse phasor-transform it to get the answer in the time domain. this is an example of a problem that is easier to solve in the frequency domain than in the time domain. use phasor techniques to find an expression for v(t) expressed as a single cosine function, where u(t) = [100 cos(300t + 45°) + 500 cos(300t – 60°)] v. enter your expression using the cosine function. round real numbers using two digits after the decimal point. any angles used should be in degrees. ivo asp u vec vec o ? (t) =

ansver
Answers: 3

Other questions on the subject: Engineering

image
Engineering, 03.07.2019 14:10, aliceohern
The y form of iron is known as: a) ferrite b) cementite c) perlite d) austenite
Answers: 3
image
Engineering, 04.07.2019 18:10, leomessifanboy678
The filament of an incandescent lamp has a temperature of 2000k. calculate the fraction of radiation emitted in the visible light band if the filament is approximated as blackbody
Answers: 2
image
Engineering, 04.07.2019 19:10, batmanmarie2004
Afoot bridge is made as a simple deck, 4 m long, with a cross section 2 m (wide) and 20 cm thick, and made of wood. the deck is supported at the two ends. the maximum load allowable on the bridge is 10 tons, provided it is uniformly distributed on the deck. to sense this load, a strain gauge is placed at the center of the bridge and its resistance is monitored. if the sensor has a nominal resistance of 350 s2 and a gauge factor of 3.6, what is the reading of the strain gauge at maximum load? the modulus of elasticity for the wood used in the construction is 10 gpa.
Answers: 2
image
Engineering, 04.07.2019 19:10, Calliedevore
The proportional limit is always greater than the yield strength for a material. a)-trune b)- false
Answers: 3
You know the right answer?
To use the phasor transform and its inverse with sinusoidal functions. we are developing a technique...

Questions in other subjects: