(You may use the book and/or notes)In Class Assignment (15 min)

1.Find CT

2. Using VC= VS(1 - e-t/), what is the voltage across a

capacitor at 10 seconds if R = 5Ω, C=2F, and VS = 8V

3. What is the capacitance in Farads of a capacitor that has a vacuum for a dielectric, where the plates are 1mm x 1mm separated by a distance of 1m.

What is ?How many Tau does it take to get exactly charge

a capacitor to 75% of being fully charged?

How long does it take to charge a capacitor to fully charged if there is no resistor in the circuit?

A capacitor acts like a ___________ under DC conditions and an ____________ under high frequencies.

Today we will learn how capacitors and inductors act under normal frequencies

Chapter 21 Review

𝑡=−𝜏 ∙ ln (1−𝑉 𝐶

𝑉 𝑆

)

openshort

A long time constant is defined as one in which the RC time constant (τ) is at least five times longer, in time, than the pulse width of the applied waveform. As a result, the capacitor of a series RC circuit accumulates very little charge, and VC remains small.

Short, Medium, and Long ’s

Draw VC

A medium time constant is defined as one in which the RC time constant (τ), in time, is equal to the pulse width of the applied waveform. As a result, the voltage across the capacitor of a series RC circuit falls between that of a long and short time constant circuit.

Short, Medium, and Long ’s

Draw VC

An RC circuit can be used to convert a Square wave signal into a Triangle signal. Also known as an Integrator circuit.

A short time constant is defined as one in which the time constant is no more than one-fifth the pulse width, in time, of the applied voltage. Here, the capacitor quickly charges to the applied voltage and remains there until the input drops to zero. Then the capacitor quickly discharges to zero.

Short, Medium, and Long ’s

Draw VC

Capacitive and Inductive Reactance

Chapter 22

Keeping in mind:Inductors act like shorts under DC and opens at

instant change.Capacitors act like opens under DC and shorts at

instant change.An AC signal is voltage level that is constantly

changing.Both inductors and capacitors resist this mid level

voltage change. (Not 0Hz but not high freq either).Since Sine waves are continuous, this resistance is

constant.In this sense, you can say capacitors are like

constant resistors under steady AC waveforms.

AC signals

The resistance or opposition that inductors and capacitors have towards an AC signal is not called resistance, it is called REACTANCE.

Reactance for a capacitor is labeled XC.

Reactance for an inductor is labeled XL.If both resistance and reactance exist in a circuit,

then this total opposition is called IMPEDANCE:

IMPEDANCE - THE TOTAL OPPOSITION TO CURRENT FLOW.

Impedance is labeled Z

Reactance – X (symbol for reactance)

http://www.wired.com/geekdad/2011/10/dont-blink-lego-nxts-and-a-smartphone-just-solved-your-rubiks-cube/

RVOTD

Because the plates of a capacitor are changing polarity at the same rate as the AC voltage, the capacitor seems to pass AC.

Suppose you put capacitor in series with your scope probes when you were measuring voltage signal that contained both AC and DC parts. What would your oscope show?

Capacitive Reactance XC

Capacitors have LESS reactance under 2 conditions:

(What do you think they are?)1. Increase in frequency2. Increase in Capacitance

Capacitive Reactance XC

XC =

Ex: Determine the capacitive reactance XC of a 10uF capacitor when the frequency is 1kHz.

XC = Ex: Determine the capacitive reactance XC of

a .001uF capacitor when the frequency is 4kHz.

XC =

Finding Capacitive Reactance

XC =

12𝜋 1000 ∙0.000010= 15.9Ω

12𝜋 4 000 ∙.001𝑢 = 39.8kΩ

Ex: Determine the frequency of a circuit if the resulting capacitive reactance XC is 300Ω of a 500nF capacitor.

f = Ex: Determine the capacitor size if its

capacitive reactance is 1000Ω at 50kHz.C =

Finding frequency and Capacitance

XC =

= 1061 Hz

= 3nF

What is the current flowing in the circuit below?

However, this is not the whole story.Capacitors don’t act purely like a resistor. Why?There is a lag, as we will see in a few slides.

Using Reactance to find Current

XC = =132kΩ

I = 𝑉𝑋𝐶

=120132𝑘

=905𝑢𝐴

What is the current flowing in the circuit below?

Yes you could have combined the capacitors first. How would you do this?

Using Reactance to find Current

XC1 = =132kΩ

I = 𝑉𝑋𝐶

=12088𝑘

=1.36𝑚𝐴

XC2 = =265kΩ

XT = 88kΩ Once you’ve converted Capacitors into resistances, treat them like resistors when doing the math.

You can also combine all capacitors first.What would be the total capacitance in this

circuit?

Using Reactance to find Current

XC = =88kΩ

I = 𝑉𝑋𝐶

=12088𝑘

=1.36𝑚𝐴

Why is XC measure in ohms?

What is the proportionality between f and XC?

What is the proportionality between f and XC?

Capacitive Reactance Review

Capacitors have MORE reactance under 2 conditions:

(What do you think they are?)1. Increase in frequency2. Increase in Capacitance

Inductive Reactance XL

XL =

Ex: Determine the inductive reactance XL of a 10mH inductor when the frequency is 1kHz.

XL =Ex: Determine the inductive reactance XL of a

700uH inductor when the frequency is 35kHz.

Finding Inductive Reactance

H = 62.8Ω

XL =

XL = 2 π 35000 ∙700𝑢= 154Ω

Ex: Determine the frequency of a circuit if the resulting inductive reactance XL is 450Ω of a 50mH capacitor.

f = Ex: Determine the inductor size if its

inductive reactance is 1000Ω at 50kHz.L =

Finding Capacitive Reactance

= 1432 Hz

XL =

= 3.2mH

What is the current flowing in the circuit below?

However, this is not the whole story.Inductors don’t act purely resistive either. Why?There is a lag, as we will see in a few slides.

Using Reactance to find Current

XL = Ω

I = 𝑉𝑋𝐿

=50150.8

=332𝑚𝐴

Can you graph this current

The answer for current in the previous problem was 332mA.

This current would look sinusoidal if you graphed it. (Similar to voltage) It is not a flat signal.

Would this current be graphed as peak-to-peak? Peak? RMS? Average?

The Graph of an AC Current looks AC

http://www.wimp.com/meltsrock/

RVOTD

The difference between reactance and resistance is with reactance there is a delay of some sort.

Its called reactance because inductors and capacitors react to voltage changes, and it takes time to react, while resistors resist instantly as voltage changes.

Reactance is not purely resistance otherwise it would be called resistance

Inductor Capacitor Analogy Handout

Does capacitor current lead or lag capacitor voltage?

ICECurrent in a capacitor leads voltage in a capacitor

Reactance of an Inductor

Does inductor voltage lead or lag inductor current?

ELIVoltage in an inductor leads current in an inductor

ELI the ICEman

A pneumonic for remembering the leading and lagging characteristics for inductors and capacitors is:

http://www.sweethaven.com/sweethaven/modelec/dcac/basicequs/default.asp

More Practice (with white boards?)