Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd



Download 5,69 Mb.
Pdf ko'rish
bet335/427
Sana21.11.2022
Hajmi5,69 Mb.
#869982
1   ...   331   332   333   334   335   336   337   338   ...   427
Bog'liq
Electric Circuit Analysis by K. S. Suresh Kumar

IntroductIon
A circuit containing a single linear time-invariant capacitor and a linear time-invariant resistor, excited 
by a voltage source in series or a current source in parallel, will constitute a first-order LTI circuit. 
We have studied a first-order circuit – namely, the RL Circuit – in great detail and used it to bring out 
all the important concepts in the time-domain analysis of electrical circuits in the last chapter. Hence, 
we will be able to move through simple RC circuits rather quickly in this chapter. That does not mean 
that RC circuits are less important in any sense compared to RL circuits. RLRC and RLC circuits are 
basic building blocks of electrical and electronic circuits and are equally important. It is only that we 
chose to deal with RL circuits first and that in no way makes other dynamic circuits less important.
11.1 
RC
 cIrcuIt EquatIons
First-order Series RC Circuit and Parallel RC Circuit are shown in Fig. 11.1-1 with all element variables 
identified. We choose the voltage across capacitor, v
C
(t), as the describing variable in both cases. If 
v
C
(t) is known in the series circuit, the current through capacitor can be obtained by multiplying the 
first derivative of v
C
(t) by C. Then the current through the resistor and voltage across it may be found. 
Similarly, all other element variables in the Parallel RC Circuit can be found out if v
C
(t) in that circuit 
is known.
Chapter 
11


11.2


First-Order
RC
Circuits
(a)
+
+
+



C
R
v
S
v
C
i
R
i
C
v
R
(b)
+
+


C
R
i
S
v
C
i
R
i
C
v
R
Fig. 11.1-1 
1(a)Theseries
RC
circuit(b)Theparallel
RC
circuit
The differential equation governing the Series RC Circuit is obtained by applying KCL at the 
positive terminal of the capacitor along with element equations of resistor and capacitor.
i t
i t
i t
v t
v t
R
i t
C
dv t
dt
R
C
R
S
C
C
C
by KCL
But, 
and
( )
( )
( )
( )
( )
( )
( )
=
=

=

C
C
dv t
dt
v t
v t
R
t
i e
dv t
dt
RC
v t
RC
v
C
S
C
C
C
for all 
( )
( )
( )
. ,
( )
( )
=

+
=
1
1
S
S
for all 
( )
t
t
The differential equation for the Parallel RC Circuit is obtained by applying KCL at the positive 
terminal of the capacitor.
i t
i t
i t
i t
v t
R
i t
C
dv t
dt
S
R
C
R
C
C
C
( )
( )
( )
( )
( )
( )
( )
=
+
=
=

by KCL
But, 
and
C
C
dv t
dt
v t
R
i t
t
i e
dv t
dt
RC
v t
i
C
C
S
C
C
S
( )
( )
( )
. ,
( )
( )
(
+
=
+
=
for all
1
tt
C
t
)
for all
The describing differential equation is a linear first-order equation with constant coefficients in 
both the cases. We expect the solution to contain a natural response term of e
-
a
 
t
type with 
a
=
1/RC
Comparing with the RL circuit equations, we can identify the time constant of RC circuit as RC 
seconds. 

Download 5,69 Mb.

Do'stlaringiz bilan baham:
1   ...   331   332   333   334   335   336   337   338   ...   427




Ma'lumotlar bazasi mualliflik huquqi bilan himoyalangan ©hozir.org 2024
ma'muriyatiga murojaat qiling

kiriting | ro'yxatdan o'tish
    Bosh sahifa
юртда тантана
Боғда битган
Бугун юртда
Эшитганлар жилманглар
Эшитмадим деманглар
битган бодомлар
Yangiariq tumani
qitish marakazi
Raqamli texnologiyalar
ilishida muhokamadan
tasdiqqa tavsiya
tavsiya etilgan
iqtisodiyot kafedrasi
steiermarkischen landesregierung
asarlaringizni yuboring
o'zingizning asarlaringizni
Iltimos faqat
faqat o'zingizning
steierm rkischen
landesregierung fachabteilung
rkischen landesregierung
hamshira loyihasi
loyihasi mavsum
faolyatining oqibatlari
asosiy adabiyotlar
fakulteti ahborot
ahborot havfsizligi
havfsizligi kafedrasi
fanidan bo’yicha
fakulteti iqtisodiyot
boshqaruv fakulteti
chiqarishda boshqaruv
ishlab chiqarishda
iqtisodiyot fakultet
multiservis tarmoqlari
fanidan asosiy
Uzbek fanidan
mavzulari potok
asosidagi multiservis
'aliyyil a'ziym
billahil 'aliyyil
illaa billahil
quvvata illaa
falah' deganida
Kompyuter savodxonligi
bo’yicha mustaqil
'alal falah'
Hayya 'alal
'alas soloh
Hayya 'alas
mavsum boyicha


yuklab olish