Electronics - RC Circuits - Discussion

Please explain.

Doesn't (1/333-1/250i)^-1 = 120.03 - 159.88i not 120 + 159.88i?

And I get 3.6V.

Here;

1. Get the inverse (1/333 - 1/250i)^-1 to get the impedance since it is in admittance form, then it will be equal to 120.03 + 159.88i.
2. Then next step is to add that to (180 - 240i).
3. And, (120.03 + 159.88i) + (180 - 240i) = 300.09 - 80.12i.
4. Then convert that to Polar form which is equal to 310.55 <-14.95.
5. Now the total impedance is 310.55, and by voltage divider formula Vr1 = (10/310.55)(180) = 5.8 volts.

Please explain.

I want an answer to my question.

Suppose we have a circuit where the ratio of the complex amplitude of the particular integral to the amplitude of the driving sinusoid is

VpVi = jωRC1 + jωRC.

Given that R = 0.82kΩ and C = 10.0nF we will compute the magnitude and phase of this ratio for various frequencies.

For frequency f = 170Hz what is the magnitude of VpVi?

I think here XL1 = 240 ohm not XC 1=240 ohm.

When XL 1 = 240 ohm, then calculate:

z1 = 180 + j240
z2 = 333 * -j250/(333-j250)
= 120.03 -j159.88
= 120-j160 (approx.)
z = z1 + z2
= 300 + j80

z = sqrt[(300)2 + (80)2]
=310.48 ohm = 310.5 ohm(approx.).

i = v/z = 10/310.5 = 0.0322 A.
Voltage drop across r1 = 180 * 0.0322.
= 5.79 volts.
= 5.8 volt(approx).

Also, phase angle, tan(θ) = 80/300 = 0.26666 = 0.267(approx).
So, θ = Arctan(0.267).
= 14.95 degree.

@Alex, your answer is 3.6 V. They give 5.80 V.

Which one is correct? Anybody tell me.

Let me tell in more simpler way.

R1 and XC1 are series to source. So z1 = sqrt (R1^2+XC1^2).

R2 and XC2 are parallel to source. So z2 = 1/sqrt ((1/R2)^2+(1/XC2)^2).

Then z = z1+z2. Voltage drop = R1/z*vs.

No. Just simply, no.

You guys are all doing this wrong and the answers are wrong.

You can't simply combine the parallel R2||Xc2 in the traditional method. You have to remember that capacitive reactance is at an angle of -90°.

When you combine that parallel branch, you have to convert back and forth between polar and rectangular forms as appropriate (addition in rectangular, multiplication/division in polar).

So let me walk you through this:

Req=R2||X2.
Req=333||-j250.

Req=1/((1/333)+(1/250<-90°)) <--in polar for division.
Req=1/(0.003+j 0.004) <--in rectangular for addition.

Req=1/(0.005<53°) <--Convert to a vector/rectangular.
Req=200<-53° <-- That is the equivalent resistance.

Now, convert that back to rectangular and add R1 and Xc1:

200<-53° = 120-j159.73.

Zt = (120-j159.73)+(180-j240).

Zt = 300-j400 <-- (rounded to -j400).

Zt = 500<-53° <-- (polar representation).

Now:

It = Vt/Zt=10V/500<-53°) = 0.02 A < 53°.

VR1 = It*R1 = 0.02 A*180Ω = 3.6 V.

Since the parallel combination of xc2 and R2 = 142.79.

Therefore z = square root(180^2+240^2+142.79^2) = 332.25.

Hence Vr1 = 10*180/332.25 = 5.8v.