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My book states:
"Power is proportional to amplitude squared"
How can this be derived?
Thank you!
"Power is proportional to amplitude squared"
How can this be derived?
Thank you!
I agree.One example of power vs. amplitude is electricity. We often refer to voltage or current as the amount of electricity in a load, like a resistor (R ohms). In reality, the power of the electricity in a resistor is the current-squared times R (watts), or the voltage-squared divided by R (watts). We alo talk about the product of voltage and current as power. So current or voltage are amplitudes, and the power is watts.
I think this goes way over my head. Never heard of Poynting vectors or transverse vectors.This is also true in electromagnetic waves. We talk about the transverse E vector or the H vector (amplitudes) in an electromagnetic wave. [Note that E is volts per meter and H is amp-turns per meter]. E and H are amplitudes, while the Poynting vector, which is E x H , is power (per square meter).
Can't make a lot of sense of this either.i think we have learned in the sound chapter that intensity is proportional to the amplitude.you know Intensity is more or less can be assumed to be power. power per unit area ok . we all know we can derive this by disintigrating wave equation. the plot of Voltage vs time or current vs time also give a wave diagram in graph, we can obtain wave equation from this and after certain procedure as similar that we had in sound chapter(that is relating with energy and linking with certain rate of time) that is likely to give intensity and amplitude relaton, well i am just studying 10+2 class and this is engineering topic but i have well trie to explain this
John Henry Poynting (1852-1914), one of Maxwell's students, was a professor of physics at Mason Science College, now the University of Birmingham, England. In 1884-1885 he published papers which showed that energy flow can be expressed in a simple formula using the electric and magnetic fields.I think this goes way over my head. Never heard of Poynting vectors or transverse vectors.
you can make sense nowI agree.
I think this goes way over my head. Never heard of Poynting vectors or transverse vectors.
Can't make a lot of sense of this either..
you can make sense now
you know
Amplitude means the highest position of the vibrating particle. in the graph plot of Voltage vs time or Current vs time you get sinosoidal curve, the peak yalue of current(I) is called as amplitude . i guess the amplitude in n ur book means that.look here i am doing calculation
I=Ipeak . sinwt (Ipeak=amplitude)(t=instantaneous time)
now power=I^2 .R=(Ipeaksinwt)^2 .R=Ipeak^2.sinwt^2.R=a^2.sinwt^2.R
(here a=amplitude=peak value of current=Ipeak) and that is power proportional to amplitude square)
hey guy i think u have understood now. i think there is no other clear cut way
Amrit is fundamentally correct. The language barrier is irrelevant when the math is correct, and it is.
hey topher 92 don't flaoat in maths (iamengineer)said power proportional to amplitue square and i don't understand power = A^2
, however using common sense i can tell that the amplitude that iamanengineer mentioned is the highest peak of current signal
, and surely he didnot mean the amplitude of the particles because there are no particles vibrating in electricity as in sound propagation,
i request topher925 be more physical then mathematical
p= (5coswt+10i sinwt) (5coswt-10isinwt)=(5coswt)^2-(10isinwt)^2= 25cos^2wt+100(sinwt)^2=25(1-sinwt^2)+100sinwt^2=25-75sinwt^2
, this is hellIf you don't fundamentally understand the question, then don't try to answer it.
I am not student of bachelor but i lack terminologies but not conscience
No you can't, you just made the assumption.
Assumption is the key to science(physics)
Yes there is, look up AC electrical power. I'm guessing the electrons powering your computer are vibrating back and forth 50 times a second.
i mentioned the evidence of the graph plot of the current vs time, the upper half cycle of the ac current is forth vibration of the electron and another half cycle is of back vibration of electron and calculation are all based on it
You want me to answer a question asking how something is mathematically derived without using mathematics?
are u gone out of ur mind what are u telling
Amrit, the bottom line is that your definition is only true for some simple cases, but not all. Do you understand why?
Concept is main and it applies to every complex matter
Pop Quiz:
(You can solve this with simple HS math and the definition I gave, but try yours)
i neednot solve this, i am not here to give test , i am here to help others with my hypothesis
Lets assume that the AC electricity waveform that is powering your computer can be described with the equation;
U = 5 cos(wt) + 10 isin(wt)
What is the power of this electrical waveform?