Download In Class Assignment (15 min)

(You may use the book and/or notes)
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 1m.
 What is
?
 How many Tau does it take to get exactly charge a
capacitor to 75% of being fully charged?
𝑉𝐶
𝑡 = −𝜏 ∙ ln(1 − )
𝑉𝑆
 How long does it take to charge a capacitor to fully
charged if there is no resistor in the circuit?
open under DC conditions
 A capacitor acts like a ___________
short
and an ____________
under high frequencies.
 Today we will learn how capacitors and inductors act
under normal frequencies
 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.
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. 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.
Draw VC
Capacitive and Inductive
Reactance
 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.
 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
 http://www.wired.com/geekdad/2011/10/dont-blink-
lego-nxts-and-a-smartphone-just-solved-your-rubikscube/
 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?
 Capacitors have LESS reactance under 2 conditions:
 (What do you think they are?)
 1. Increase in frequency
 2. Increase in Capacitance
XC =
1
2𝜋𝑓𝐶
[Ω]
1
2𝜋𝑓𝐶
XC =
[Ω]
 Ex: Determine the capacitive reactance XC of a 10uF
capacitor when the frequency is 1kHz.
 XC =
1
2𝜋𝑓𝐶
1
=
2𝜋1000 ∙ 0.000010
= 15.9Ω
 Ex: Determine the capacitive reactance XC of a .001uF
capacitor when the frequency is 4kHz.
 XC =
1
2𝜋𝑓𝐶
1
=
2𝜋4000 ∙ .001𝑢
= 39.8kΩ
XC =
1
2𝜋𝑓𝐶
[Ω]
 Ex: Determine the frequency of a circuit if the
resulting capacitive reactance XC is 300Ω of a 500nF
capacitor.
f =
1
2𝜋𝑋𝐶𝐶
1
=
2𝜋300∙500𝑛
= 1061 Hz
 Ex: Determine the capacitor size if its capacitive
reactance is 1000Ω at 50kHz.
C=
1
2𝜋𝑓𝑋𝐶
1
=
2𝜋50000∙1000
= 3nF
 What is the current flowing in the circuit below?
XC =
I=
𝑉
𝑅
1
2𝜋𝑓𝐶
=
1
=132kΩ
2𝜋60∙20𝑛𝐹
𝑉
120
= 𝑋 = 132𝑘 = 905𝑢𝐴
𝐶
 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.
 What is the current flowing in the circuit below?
1
1
XC1 =
=
=132kΩ
2𝜋𝑓𝐶
2𝜋60∙20𝑛𝐹
1
1
XC2 =
=
=265kΩ
2𝜋𝑓𝐶
2𝜋60∙10𝑛𝐹
132𝑘∙265𝑘
XT =
= 88kΩ
132𝑘+265𝑘
Once you’ve converted
𝑉
120
Capacitors into
𝑉
I = = 𝑋 = 88𝑘 = 1.36𝑚𝐴
resistances, treat them
𝑅
𝐶
like resistors when doing
the math.
 Yes you could have combined the capacitors first.
How would you do this?
 You can also combine all capacitors first.
 What would be the total capacitance in this circuit?
XC =
I=
1
2𝜋𝑓𝐶
𝑉
𝑅
=
1
=88kΩ
2𝜋60∙30𝑛𝐹
𝑉
120
= 𝑋 = 88𝑘 = 1.36𝑚𝐴
𝐶
 Why is XC measure in ohms?
 What is the proportionality between f and XC?
 What is the proportionality between f and XC?
 Capacitors have MORE reactance under 2 conditions:
 (What do you think they are?)
 1. Increase in frequency
 2. Increase in Capacitance
XL = 2π𝑓𝐿 [Ω]
XL = 2π𝑓𝐿 [Ω]
 Ex: Determine the inductive reactance XL of a 10mH
inductor when the frequency is 1kHz.
 XL =2π𝑓𝐿 = 2π1000 ∙ 10𝑚H = 62.8Ω
 Ex: Determine the inductive reactance XL of a 700uH
inductor when the frequency is 35kHz.
XL =2π𝑓𝐿 = 2π35000 ∙ 700𝑢 = 154Ω
XL = 2π𝑓𝐿 [Ω]
 Ex: Determine the frequency of a circuit if the
resulting inductive reactance XL is 450Ω of a 50mH
capacitor.
f =
𝑋𝐿
2𝜋𝐿
=
450
2𝜋50𝑚
= 1432 Hz
 Ex: Determine the inductor size if its inductive
reactance is 1000Ω at 50kHz.
L=
𝑋𝐿
2𝜋𝑓
1000
=
2𝜋50𝑘
= 3.2mH
 What is the current flowing in the circuit below?
XL = 2𝜋𝑓𝐿 = 2𝜋800 ∙ 30𝑚 = 150.8Ω
I=
𝑉
𝑅
𝑉
50
= 𝑋 = 150.8 = 332𝑚𝐴
𝐿
Can
you
 Inductors don’t act purely resistive either. Why? graph
 There is a lag, as we will see in a few slides.
this
current
 However, this is not the whole story.
 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?
 http://www.wimp.com/meltsrock/
 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.
Does capacitor current lead or lag capacitor voltage?
ICE
Current in a capacitor leads voltage in a capacitor
Reactance of an Inductor
Does inductor voltage lead or lag inductor current?
ELI
Voltage in an inductor leads current in an inductor
A pneumonic for remembering the
leading and lagging characteristics for
inductors and capacitors is:
ELI the ICEman
 http://www.sweethaven.com/sweethaven/modelec/dc
ac/basicequs/default.asp