Wt Pc

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College Physics-ELECTROMAGNETIC OSCILLATIONS & AC?

I have 5 questions in all, here are the links to them:

http://i152.photobucket.com/albums/s167/gt_badone/31-61.jpg

I need formulas more than answers, if you are going to give me answers (don't need solution) be sure to provide formulas!

Ok, for the first problem, we don't need to solve the circuit, but we need to remember some theory :

For a AC, circuit : Ir = Im*sen(wt)

Im = Vm / R

P = Im^2*R*sen^2(wt)

That's for the resistor.

For the inductance :

L = Vm / Lw*sen(wt)

and : XL = W.L >>> inductive reactance

VL = Vmsen(wt) = Im.XL*sen(wt)

For the capacite :

ic = dQ / dt = CVmwcos(wt)

ic = wcVmsen(wt) >>> Vc = Vmsen(wt)

XC = 1 / wc >>>>> Capacitance reactance

So, for the whole circuit :

Vm = sqrt((VL - Vc)^2 + Vr^2))

Vr = Im*R
VL = Im*XL
Vc = Im*Xc

Vm = Im*sqrt((XL - Xc)^2 + R^2))

So for the first problem :

E = 40.1*sen(3910)t

Xc = 1 / wc = 1 / 3910*24.3*10^6 = 10.52 = Xc

XL = w.L = 3910*7.47*10^-3 = 29.2 = XL

Vm = E = 40.1

then using :

Vm = Im*sqrt((XL - Xc)^2 + R^2))

40.1 = Im*sqrt((29.2 -10.52)^2 + 23.9^2)

Im = 1.32 Amperes

Now using :

Vr = Im*R >>>> Vr = 1.32*23.9 = 31.5

VL = Im*XL>>>VL = 1.32*29.2 = 38.5

Vc = Im*Xc>>>Vc = 1.32*10.52 = 13.8

I = Im*sen(wt)

I = 1.32*sen(3910t)

for t = 0.526 s

we can find : P = Im^2*R*sen^2(wt)

P = 1.32^2*23.9*sen^2(3910*0.526)

Pr = 39.4 (Watts)

Now, let's find Pc :

I = 1.32*sen(3910t)

Pc = 1/2*C*E^2*sen^2(wt)

Pc = 1/2*24.3*10^-6*(40.1)^2*sen^2(3910*0.522) = 0.018 Watts.

Well, It was kind of long.

Second problem : Hope you understand, again :

Here you have to calculate : VL, Vc and Vr :

First of all, we calculate : Xc and XL

XL = W.L >>> inductive reactance

VL = Vmsen(wt) = Im.XL*sen(wt)

For the capacite :

ic = dQ / dt = cVmwcos(wt)

ic = wcVmsen(wt) >>> Vc = Vmsen(wt)

XC = 1 / wc

Vr = Im*R
VL = Im*XL
Vc = Im*Xc

Given : Frequency = 512 Hz >>> w = 1024*pi

R = 14,5

L = 25.4*10^-3

C = 3.75*10^-6

Vm = 104

V = 104sen(1024*pi*t)

XL = WL = 1024*pi*25.4*10^-3 = 81.7

Xc = 1 / wc = 1 / 1024*pi*3.75*10^-6 = 82.9

using : Vm = Im*sqrt((XL - Xc)^2 + R^2))

104 = Im*sqrt((XL - Xc)^2 + R^2))

Im = 7.14 Amperes

VL = 7.14*81.7 = 583

Vc = 7.14*82.9 = 592

Vr = 7.14*14.5 =103.53

That's it, you have the current, and the voltage in every component, C, L and R.

Third problem.-

This one is very easy, just remember :

N2*V1 = N1*V2

so then : 100*610 = 51*V2

V2 = 1196 volts

Fourth problem .-

Transformers :

N1 = 470 turns

N2 = 9.6 turns

Vp = 120

Using the same formula :

470*V2 = 9.6*120

V2 = 2.45 volts

rms V2 = 2.45sen(wt)

second part : Secondary has a resistor of 20 ohms

remeber : V1*I1 = V2*I2

secondary has a 20 ohm resistor, then : I2 = 2.45sen(wt) / 20

I2 = 0.12sen(wt)

then : 120sen(wt)*I1 = 0.12sen(wt)*2.45sen(wt)

I1 = 2.45*10^-3sen(wt) amperes

Fifth question .- Last problem

It's like the first problems, a series circuit, RLC :

We just have to find the Vc, VL, and Vr, the voltage on every part of the circuit :

XL = W.L

Xc = 1 / wc

w = 120*pi

R = 280

L = 270*10^-3

C = 20.4*10^-6

Vm = 42

V = 42sen(wt)

Xc = 1 / 120*pi*20.4*10^-6 = 130

XL = 120*pi*270*10^-3 = 101.8

Using : Vm = Im*sqrt((XL - Xc)^2 + R^2))

Im = 0.15 amperes

Vc = 0.15*130 = 19.5

VL = 0.15*101.8 =15.27

Vr = 0.15*280 = 42

Hope that might help you

Note : Im = maximum current

Vm = maximum voltage

C= capacitor o capacite

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