Electronic Circuit Question.

Thread Starter

RRITESH KAKKAR

Joined Jun 29, 2010
2,829
What is the angle theta value for a 5.6
F capacitor and a 50-ohm resistor in series with a 1.1 kHz, 5 Vac source?

C=5.6uF
R=50ohm
F=1.1*10^3Hz
Vac=5V
Angle=?
Xc=1/2*3.14*f*C
Xc=1/6.28*1.1*1000*5.6*10^-6
Xc=25.84ohm
Toal Z=√(R²+Xc²)
Z²=50²+25.84²
Z=56.28ohm


........
 
how to find it?
The answer is –27.3 degrees
TanQ=Xc/Xr
=25.84/50=0.8168
Q=27.3
not cumming negative.
Firstly 'Xr' makes No sense!
Secondly
Inasmuch as you are solving for an angle -- an inverse trig function may be useful
Thirdly The sign on the reactance (and, hence, the 'phase shift') is down to the reactor type

So:

R=50Ω
Xc=1/(2*Π*1100*5.6*10^-6) ≈ 25.837Ω
Hence X ≈ -25.837Ω (Because capacitive reactance is taken to be 'negative')

Thus Θ≈The ArcTangent of (-25.837/50)≈-27.3272° -- Got it???

No more looking up answers! Grrrrrrrr!!!:mad::mad::mad::mad:
 
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Indeed! -- I showed him that here::)

Firstly 'Xr' makes No sense!
Secondly
Inasmuch as you are solving for an angle -- an inverse trig function may be useful
Thirdly The sign on the reactance (and, hence, the 'phase shift') is down to the reactor type
So:
R=50Ω
Xc=1/(2*Π*1100*5.6*10^-6) ≈ 25.837Ω
Hence X ≈ -25.837Ω (Because capacitive reactance is taken to be 'negative')

Thus Θ≈The ArcTangent of (-25.837/50)≈-27.3272° -- Got it???

No more looking up answers! Grrrrrrrr!!!:mad::mad::mad::mad:

I think he's got it -- if not - perhaps he'll take your word for it:D
 
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@RRITESH KAKKAR

You have, upon multiple occasions, indicated a desire for practically applicable problems -- So... I offer the following exercise in impedance transformation -- Please note that, owing to the stipulation of a two reactor network (and, hence, necessary dependence of Q) and to the fact that one of the termination impedances is pure real (i.e. pure resistive ) this is a trivially basic problem! --- Rest assured that you have demonstrated the requisite skills! -- That said you will need to THINK on how to apply said skills to this exercise!:)

So, to the exercize:
---------------------------------------------------------------------------------------------------------------------------------------------
Port 1 is is comprised of a 6Ω resistor in series with an inductor exhibiting 4Ω of reactance
Port 2 is merely a 50Ω resistor.

Match port 1 to port 2 using a network comprised of two lumped reactors... (said network to interviene terminals 'p1' and 'p2' as per the image (below)

What are the reactances of the network reactors and how are they connected?
---------------------------------------------------------------------------------------------------------------------------------------------

Special thanks to @Aleph(0) for her suggestion of an exercise of this type:)
NetEx.jpg


Best regards
HP

 
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WBahn

Joined Mar 31, 2012
29,979
AC = Alternating Current (granting that said 'stipulation' would seem implicit)



Correct! -- 'Tho leaving the solution in radical notation (i.e. 20*√5) is 'prettier':)

Best regards
HP:)
While I understand your penchant for exact answers, in practice most scientific and engineering problems report final results in decimal form. The exception being results that are focused on exact theoretical results, which are usually parameterized. For instance, the formula converting from the amplitude of a sine wave to the RMS value is almost always given with √2 in it. But the results of actually applying that formula seldom are.

The reasons basically come down to two factors: (1) Engineering is (generally) about real world quantities and all such quantities have tolerances that render exact representations either extraneous or downright misleading, and (2) the results are often used for comparative purposes. For instance, which is larger: 20*√5 0r 25*√3? I couldn't tell at first glance and I suspect few people could. But if asked which is larger: 44.7 or 43.3? Even most second or third graders could answer it immediately.
 
While I understand your penchant for exact answers, in practice most scientific and engineering problems report final results in decimal form. The exception being results that are focused on exact theoretical results, which are usually parameterized. For instance, the formula converting from the amplitude of a sine wave to the RMS value is almost always given with √2 in it. But the results of actually applying that formula seldom are.

The reasons basically come down to two factors: (1) Engineering is (generally) about real world quantities and all such quantities have tolerances that render exact representations either extraneous or downright misleading, and (2) the results are often used for comparative purposes. For instance, which is larger: 20*√5 0r 25*√3? I couldn't tell at first glance and I suspect few people could. But if asked which is larger: 44.7 or 43.3? Even most second or third graders could answer it immediately.
Fair enough!:) --- Seems all this 'bouncing about' between math and engineering (well... electronics) has me 'on the ropes' as it were!:eek::eek::eek::D

Best regards
HP:)
 
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Port1 Z=√(Xr²+Xl²)=√(36+16)=7.21ohm
Port2 Z=50ohm

now what to do?
Again, "resistive reactance" makes NO SENSE! --- I never want to see 'Xr' again!!!:mad::mad::mad: Ok?;)

Port1 Z=√(Xr²+Xl²)=√(36+16)=7.21ohm
Inasmuch as you seem determined to take a 'pedestrian' approach - just match the real components then compensate for port reactance via adjustment of the network reactor{s} -- Please note that, in this exercise, only port 1 contains reactance...

Please note:
Inasmuch as I have not specified network filter behaviour -- there are, in essence, two network configurations satisfactory of the stipulations -- I will accept either one as a correct reply:):):)

--Sledgehammer hint--
Re: Two reactor networks -- As may should be obvious:
System Quality Factor (Q) = √(transformation_ratio-1) {transformation_ratio|transformation_ratio>1}

Please 'dwell' on it! --- The implications of this are 'huge'!!!:cool::cool::D


Best regards
HP:)
 
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