ENG1002 Lecture Notes - Lecture 10: Short Circuit, Voltage Source
30 May 2018
School
Department
Course
Professor
RC#circuits ="contain"sources"and"resistors
Discharging
Capacitor"with"capacitance"C initially"
charged"to"a"value"VC(0)"="Vi@"t"="0
1.
Switch btwn"capacitor"and"resistor"R"closes
Charge"stored on"capacitor"
discharges around"circuit"through"
resistor
a.
2.
iC+"iR="0
VC"cannot change"
discontinuously
•
Eg."t"="0
If"it"could,"iC(t)"="±∞ -->"not"
possible
Acc."to"capacitor"I-V"
relationship
○
•
DC#steady#state analysis
t"="0
Week$10:$RC$circuits
Sunday,"7"May"2017
15:32
Time#constant
63%"of"full"voltage.
VC(t)"proportional"to"Q"[Q"="CV,"constant"
until"t"="0"when"switch"closes]
•
@"t"="τ-->"CVdecayed"by"factor"of"e-1 (~
0.368)
•
@"t"="5τ-->"CVdecayed"practically"to"zero
•
Transient response
Steady#state#response
@"VC"(∞)"="0
Graph"of
t"="0
Switch"has"been"open"for"
a"long"time
•
VChas"reached"steady"
state
Capacitor"doesn't"
conduct"any"current
○
Capacitor"acts"like"
open"circuit
○
•
Opening the#switch
VC(0)"="0
VC(∞)"="VCC
Solution:
Time#constant#calculation
When"calculating"time"constant,"
must"use"single"value"of"resistance
Thevenin's"Theorem!
There"are"2:"
(for"charging"circuit)
(for"discharging"circuit)
Carefully"choosing"values"for"
capacitors"and"resistors allows"us"
to"control"time"taken"to"charge"
and"discharge capacitor
Eg:
Closing the#switch
VC(0-)"="VCC
VC(0+)"="VCC"[due"to"capacitor"
voltage"continuity]
Circuit"that"is"hooked"up"must:
measure"VCthat"will"
•
Document Summary
Capacitor with capacitance c initially charged to a value vc(0) = vi @ t = 0. Switch btwn capacitor and resistor r closes a. Charge stored on capacitor discharges around circuit through resistor. If it could, ic(t) = --> not possible. Dc steady state analysis ic + ir = 0 t = 0 t = 0. Switch has been open for a long time. When calculating time constant, must use single value of resistance. There are 2: (for charging circuit) (for discharging circuit) Carefully choosing values for capacitors and resistors allows us to control time taken to charge and discharge capacitor. Vc(t) proportional to q [q = cv, constant until t = 0 when switch closes] @ t = --> cv decayed by factor of e-1 (~ @ t = 5 --> cv decayed practically to zero. Vc(0+) = vcc [due to capacitor voltage continuity]
