ch 21 pt 2 and ch 22

if the resistance R is equal to the inductive reactance X_L in an RL circuit, what is the power factor?

0.707

what is the power factor at the resonant frequency of an RLC circuit?

1

omega =

2pif

the current lags the voltage by a phase angle of

90 degrees

purely resistive AC: I= V/R becomes

I= V/R = Vo/r x sin(2pif) = Io x sin(2pif)

Vo=

NBA x omega

when phi=0 (such as at resonant f), R/Z=

R/Z equals 1 cos(0)=1

the power factor is

cos(phi)

in the phasor model, the voltage and current are represented by arrows called phasors that rotate

counterclockwise in an xy coordinate system

when a capacitor is connected to a DC source,

current doesn't flow once its charged

purely resistive AC circuit: when voltage increases,

current increases (directly related)

the magnetic flux through the inductor changes as the

current is changing

B changes as a function of time because

current is changing as function of time

the *vertical component* of the phasor is the instantaneous value of the

current or voltage V(t)=Vosin(2pift) I(t)=Iosin(2pift)

why?

current switches directions (I don't quite understand)

review: electric charges generate

electric fields (stationary charges generate only E fields)

two straight wires connected to the terminals of an AC generator can create an

electromagnetic (EM) wave

the net result of these interacting changing fields is a wave of E and B fields that can propagate through space. This wave is called an

electromagnetic wave

the change in magnetic flux induces an

emf

review: moving magnets generate

emf (since emf is a voltage, it basically gnerates E-field)

Irms depends on the frequency. it will be a max when Xc=Xl; the frequency this occurs at is ____ and is called the ____

f_0= (1/2pi)*sqrt[(1/LC)]; resonant frequency (Z will have its minimum value)

phasors rotate at a constant

frequency (or angular speed of 2pif)

XL is proportional to the

frequency of the AC voltage

a bulb is connected to a 60 Hz voltage source and glows with a certain brightness (1). A capacitor is then placed in series with the bulb (2). will the brightness of the bulb:

how is the current changed? 1. Irms= Vrms/R 2. Irms=Vrms/(Z) R1<R2 I1>I2 bulb dims

the current leads the voltage across the capacitor by 90 while being

in parallel with V_R

for a purely resistive circuit, the current and voltage are

in phase

Xc unit

is ohm (resistance)

the charge Q on the capacitor Q=CV, so

it is in phase with the voltage

how will the total impedance of an RC circuit change if the frequency is decreased?

it will increase

if the frequency of the AC voltage is increased, how will the current and voltage phasors change for a capactior?

length increases

maxwell also discovered: changing electric field (not just current) gives rise to

magnetic field

review: magnets generate

magnetic fields (stationary magnets- only B field)

An AC generator converts ____ into _____

mechanical energy into electric energy

phasor model can be used to determine voltage current relationship in

more complex circuits

the field is created first near the wires and then, like the effect of a pebble dropped into a pond,

moves outward

In an RL circuit, the voltage across the resistor and inductor are

not in phase

in an RC circuit, the voltage across the resistor and the voltage across the capacitor are

not in phase (note: Vr and I are in phase while Vc and I are out of phase)

Z (impedence) has a unit of

ohm

unit of XL is

ohm -inductive resistance

for a capacitor, the phasors remain

perpendicular while rotating because the phase angle between the current and the voltage is 90. Also, the current is ahead of the voltage.

for an inductor, phasors remain

perpendicular. voltage leads.

the current leads the voltage across the capacitor by a

phase angle of 90 degrees (1/4 of cycle or T)

most importantly, maxwell's four equations can be put together to

predict waves

James Clerk Maxwell (1831-1879) was the first to put together the four equations that

quantitatively relate electric charge, electric current, electric fields, and magnetic fields

the resistance in a purely resistive circuit has the ____ value at all frequencies

same

the induced emf in a rotating coil. varies

sinusoidally emf= NBAomega x sin(omega x t) *radians/second

Z also =

sqrt[R^2 + (1/2pifC)^2]

RLC: total impedance Z=

sqrt[R^2 + (Xl-Xc)^2]

Z=

sqrt[R^2 + Xc^2]

the voltages across the inductor and across the resistor are at 90 in the diagram; if they are added as vectors we find the total voltage: Vo=

sqrt[Vro^2 +Vlo^2] = Io*sqrt[R^2 + Xl^2]

RLC Circuit Vo=

sqrt[Vro^2+(Vlo-Vco)^2] = Io*Z

the average power used by a capacitor in an AC circuit is zero,

the capacitor alternately absorbs and release energy --> 1/2 of time P is +, 1/2 of time P is - --> 1/2 time capacitor absorbs E, 1/2 time capactior releases E --> avg P dissipated by capactior= 0

the magnetic fields created at earlier times propagate outward as a wave, just as

the electric fields do

what is not true of a capacitor in an AC circuit: its instantaneous voltage equals

the instantaneous current time the capacity reactance

the length of the voltage (current) phasor corresponds to

the max voltage (current)

An electric field is generated when

there are opposite charges on the two wires *good explanation in 3/5 video 2* *diagram of switching current and charges*

electromagnetic waves can be produces in situations that do not involve a

wire antenna

the power is as often positive as it is negative: the average power used by an inductor in an ac circuit is

zero (half stored E, half released E)

what will not generate EM waves?

a steady direct current (DC) -bc charge moves in constant speed AND in one direction

when a capacitor is connected to an AC source,

an alternating current will flow continuously

there is a phase angle between the overall voltage and the current cos(phi)=

V_Ro/V_o cos(phi)= IoR/IoZ cos(phi)= R/Z

the voltage across the capacitor and across the resistor are at 90 in the diagram; if they are added as vectors, we find the total voltage:

Vo= sqrt[VR0^2+Vc0^2] Vo=sqrt[(IoR)^2+ (IoXc)^2] Vo=Io[R^2 + Xc^2]

RLC: phase angle between current and total voltage tan(phi)=

(Vl-Vc)/Vr tan(phi)= (Xl-Xc)/R

emf= -N(delta phi/ delta t)... for an inductor in a circuit is

-L(delta phi/ delta t)

When Xl=Xc, tan(phi)=

0 and phi=0 total voltage and current phasor are in phase (parallel) -Vl and Vc cancel -total V = V across resistor

Xc=

1/(2pifC)

The current reaches its peak _________ the voltage does

1/4 cycle AFTER

1 period is

360 degrees

A 10 ohm resistor is connected to a source of AC voltage. if the peak current through the resistor is 1 A, what is the average power dissipated by the resistor

5 W

by going point by point in this manner, the time dependent voltage and current curves can be constructed

:)

review: moving charge (current) generates a

B field

if a changing B-field produces an E-field, that E-field is itself changing. This changing E-field will, in turn, produce

B-field, which will be changing, and so it too will produce a changing E-field and so on

in extreme case when f=0, V is not changing as function of time, T= infinity-->

DC circuit w/ capacitor! (Xc=> infinity) (current becomes zero)

an inductor is usually a coil of wire, and the basis of its operation is

Faraday's law of electromagnetic induction

RL: Vo=

Io*Z (Vrms= Irms*Z)

therefore, Vo=

Io*Z -same form as V=IR for DC circuits (Vrms=Irms*Z)

if the value of the capacitance is doubled but the peak voltage remains unchanged, the peak current is

Io= Vo/Xc Xc= 1/(2pifc) Xc is halved Current is doubled!

RLC: avgP=

Irms^2*R = Irms(Vrms/Z)R = Irms(Vrms)cos(phi)

what will happen to the light bulb if the frequency is doubled? Circuit 1: F, L, AND R Circuit 2: 2F, L, AND R

P=Irms^2*R Irms= Vrms/Z Irms= Vrms/sqrt[R^2 + 2pifL)^2] Irms decreases, P dec, I dec -> light dims

according to the above equation, the current I is increasing most rapidly when

V has its peak value V0 (point d). The current I will be decreasing most rapidly when V= -Vo (point b)

kirchoff's loop rule for a circuit with just L and an AC generator

V+emf=0 V=-emf= L(delta I/delta t) delta I/delta t= V/L Vapplied= Vosin2pift

XL=

V0/I0 = sqrt[2]*Vrms/sqrt[2]*Irms =2pifL -must be peak or rms not valid at any point

resonant frequency Irms=

Vrms/sqrt[R^2] Z=R -minimum Z and max Irms

the relationship between RMS V and RMS I for Capacitor AC circuits

Vrms= Irms*Xc (also Vo= Io * Xc) --> this is not valid at any instant --> depends on the Xc value and frequency of oscillating voltage

if no inductor, L=0 means Z= ? and cos(phi)=? phi=?

Z=R, cos(phi)=1, phi=0

the current used to generate the electric wave creates

a magnetic field

the electric current I through the inductor produces

a magnetic field through itself

in general, any electric charge that is _________ emits an electromagnetic wave

accelerating

the average power of a purely resistive AC circuit

avg P= IrmsVrms avg P= (IoVo)/2 (power is always positive bc V and I are in phase)

the magnetic field oscillates perpendicular to

both electric field and direction of wave travel

Xc is

capacitive reactance

the graph shows the voltage across the current through a single circuit element connected to an ac generator. what is the circuit element? -curve shows a higher peak voltage than current -voltage curve moves "slower" than the current -differ by 1/4 period

capacitor

as the oscillating current changes, the magnetic field

changes accordingly

inductive reactance relates the peak (and rms) voltage to the

peak (and rms) current

V/L=

delta I/ delta t

for a resistor, the current and voltage phasors remain ____ while rotating bc they're in phase

parallel