Chapter I
dW
v = Where v =
voltage (v) ,
w =
energy (5) q= charge (c)
de
,
i =
9 where i= current (A) , q =
charge (2) ,
+
=
time (s)
Passive sign convention
:
when reference direction for current in an element is in direction of reference voltage drop
the element positive in otherwise ,
across , use sign any espression that relates the voltage to the current , negative sign .
- =
qY where =
power (W) ,
=
energy (5) ,
+= time (s) Interpreting sign of power :
p = vi where =
power (W) ,
v =
voltage (v) ,
i =
current (A) · if p>0 , power is absorbed by circuit element .
if Pco is delivered
·
, power by circuit element .
Chapter 2
Ideal voltage source : maintains a prescribed voltage across its terminals regardless of the current flowing in those terminals .
Ideal current source : maintains a prescribed current across its terminals regardless of the voltage across those terminals .
~ further described as either (p956 +
57 for symbols)
Independent source :
establishes a voltage or current in a circuit without relying on voltages or currents elsewhere in the circuit .
Dependent source :
establishes a voltage or current whose value depends on the value of a
voltage or current elsewhere in the circuit .
Ohn's law
:
V =
iR (1) v = -
iR(z) (1)
- 12
- i-
R
Resistance measured in ohm (-2) .
v
Power can be calculated in terms of resistance :
p = iR or =
Note : resistors always absorb power .
R
Kirchhoff's law sum all currents circuit equals
:
current of at
any node in a zero .
d
-
Ohm's law :
KCL :
-
for in
t
t
·
V,
=
i, R , & a :
is -
i =
0 a di iz -
is =
0
in
-
Vs R2
-
is
·
Vc icRc abii ic 0 Note is z =-ic i,
=
+ : =
=
i'
= =
,
-
-
⑧ ⑧ ⑧ ·
V
=
izRz ·ac : -
i iz -
= 0
a D C
Ri Rc
Kirchhoff's voltage law all voltages closed path in circuit equals
:
sum of around a zero
any .
d
-
KVL : + for voltage drop
Vs
t it R2
.
-
Vs
+
Vz -
V +
V,
=
0
-
-
·
-
v
t V -
⑧ ⑧ ⑧
a D C
R, Ru
, Chapter 3
Resistors in series :
two elements connected at a
single node .
2025 R4
Series connected circuit elements the
carry same current
·
⑧ ⑧
iss
-I
,
is' in
... is =
is is is is is is
Vst
X
-
15
is R3
-
Ohn's law lets us combine resistors in series ,
se eis
Req R R Rz R4 25 Ro B Vs isReq
= +
+ + =
, + +
· ⑧
Ri R2
combining resistors in series Rea Ri R , +R RK
:
=
+
...
!
Resistors in parallel :
two elements connected at both their nodes .
·Parallel connected circuit elements carry the same voltage across their terminals
:
This
Note : R, 3 Ry are not in parallel ,
but R, 3 Re are .
vs ! R4
in in law lets
·
Ohm's also us combine resistors in parallel ,
⑧
b
is reg =
a a's as ac
Combining resistors in parallel
:
Req= si =
a +
xc + .. +
ex
Voltage devider circuit :
Current divider circuit:
-
! I
vs
R,
-
, Ve iRz ,
V
M ,
2
+
2
is
i =
,mis
e vin
? mis
I
Rz -
V2 v i Voir is =
Produces two or more smaller voltages Splits current between two or more resistors .
from a
single voltage supply .
Voltage devision
:
vi
=
iRi =
Beg current devision
:
ij =
=
?? :
T
A
Ammeter placed in series with circuit element whose is
being measured
:
a current .
A
V
Voltmeter :
placed in parallel with a circuit element whose voltage is
being measured .
Wheatstone bridge :
used to determine an unknow resistors resistance .
·
R ,, R2 , &3 are known 4 R is unknown .
We adjust y until
V
there is no current in the
galvanometer (ammeter) ,
then
· Rx =
!3
, 3
Delta-to-Wye (Pi-to-Teel equivalent circuits used
simplify complexe circuits
:
to transform .
Ru
·-
b
A ·
-
R,
!
Rb Ra
·
for to Y : For Y to :
R bRc R , Rz +
R2R3 +
RaR ,
R,
=
= ·
·
Ra
R at Rb +
R R,
R . Ra R , Rz RzR
· = ·
+ +
RaR ,
R R =
Ra R >
+
+
Rz
Rab R, R 2 +
R2R3 +
R3R ,
· · Ri
=
R3
Ra R Rc
=
R3
+
+
Chapter 4
Planar circuit circuits that can be drawn on a plane with no
crossing branches .
Nonplanar circuit circuits that not be drawn plane in that there are no branches
can on a such a
way crossing .
Terminology :
node :
point where two or more circuit elements join .
essential node
:
point where three or more circuit elements join .
path
:
a trace of adjoining basic elements with no elements included more than once .
branch path that connects two nodes
:
a .
· essential branch :
a path that connects two essential nodes without passing through an essential node .
loop : a path whose last node is the same as the starting node .
mesh a loop that does not enclose other
any loops
:
.
How equations ?
many
count number of essential nodes , ne
count number of essential branches be where current is unknown .
, ,
write ne-l equations by applying KCL to
any set of re-l nodes .
write be cre-ll equations by applying KVL around a set of be-(re-1) loops or meshes .
dW
v = Where v =
voltage (v) ,
w =
energy (5) q= charge (c)
de
,
i =
9 where i= current (A) , q =
charge (2) ,
+
=
time (s)
Passive sign convention
:
when reference direction for current in an element is in direction of reference voltage drop
the element positive in otherwise ,
across , use sign any espression that relates the voltage to the current , negative sign .
- =
qY where =
power (W) ,
=
energy (5) ,
+= time (s) Interpreting sign of power :
p = vi where =
power (W) ,
v =
voltage (v) ,
i =
current (A) · if p>0 , power is absorbed by circuit element .
if Pco is delivered
·
, power by circuit element .
Chapter 2
Ideal voltage source : maintains a prescribed voltage across its terminals regardless of the current flowing in those terminals .
Ideal current source : maintains a prescribed current across its terminals regardless of the voltage across those terminals .
~ further described as either (p956 +
57 for symbols)
Independent source :
establishes a voltage or current in a circuit without relying on voltages or currents elsewhere in the circuit .
Dependent source :
establishes a voltage or current whose value depends on the value of a
voltage or current elsewhere in the circuit .
Ohn's law
:
V =
iR (1) v = -
iR(z) (1)
- 12
- i-
R
Resistance measured in ohm (-2) .
v
Power can be calculated in terms of resistance :
p = iR or =
Note : resistors always absorb power .
R
Kirchhoff's law sum all currents circuit equals
:
current of at
any node in a zero .
d
-
Ohm's law :
KCL :
-
for in
t
t
·
V,
=
i, R , & a :
is -
i =
0 a di iz -
is =
0
in
-
Vs R2
-
is
·
Vc icRc abii ic 0 Note is z =-ic i,
=
+ : =
=
i'
= =
,
-
-
⑧ ⑧ ⑧ ·
V
=
izRz ·ac : -
i iz -
= 0
a D C
Ri Rc
Kirchhoff's voltage law all voltages closed path in circuit equals
:
sum of around a zero
any .
d
-
KVL : + for voltage drop
Vs
t it R2
.
-
Vs
+
Vz -
V +
V,
=
0
-
-
·
-
v
t V -
⑧ ⑧ ⑧
a D C
R, Ru
, Chapter 3
Resistors in series :
two elements connected at a
single node .
2025 R4
Series connected circuit elements the
carry same current
·
⑧ ⑧
iss
-I
,
is' in
... is =
is is is is is is
Vst
X
-
15
is R3
-
Ohn's law lets us combine resistors in series ,
se eis
Req R R Rz R4 25 Ro B Vs isReq
= +
+ + =
, + +
· ⑧
Ri R2
combining resistors in series Rea Ri R , +R RK
:
=
+
...
!
Resistors in parallel :
two elements connected at both their nodes .
·Parallel connected circuit elements carry the same voltage across their terminals
:
This
Note : R, 3 Ry are not in parallel ,
but R, 3 Re are .
vs ! R4
in in law lets
·
Ohm's also us combine resistors in parallel ,
⑧
b
is reg =
a a's as ac
Combining resistors in parallel
:
Req= si =
a +
xc + .. +
ex
Voltage devider circuit :
Current divider circuit:
-
! I
vs
R,
-
, Ve iRz ,
V
M ,
2
+
2
is
i =
,mis
e vin
? mis
I
Rz -
V2 v i Voir is =
Produces two or more smaller voltages Splits current between two or more resistors .
from a
single voltage supply .
Voltage devision
:
vi
=
iRi =
Beg current devision
:
ij =
=
?? :
T
A
Ammeter placed in series with circuit element whose is
being measured
:
a current .
A
V
Voltmeter :
placed in parallel with a circuit element whose voltage is
being measured .
Wheatstone bridge :
used to determine an unknow resistors resistance .
·
R ,, R2 , &3 are known 4 R is unknown .
We adjust y until
V
there is no current in the
galvanometer (ammeter) ,
then
· Rx =
!3
, 3
Delta-to-Wye (Pi-to-Teel equivalent circuits used
simplify complexe circuits
:
to transform .
Ru
·-
b
A ·
-
R,
!
Rb Ra
·
for to Y : For Y to :
R bRc R , Rz +
R2R3 +
RaR ,
R,
=
= ·
·
Ra
R at Rb +
R R,
R . Ra R , Rz RzR
· = ·
+ +
RaR ,
R R =
Ra R >
+
+
Rz
Rab R, R 2 +
R2R3 +
R3R ,
· · Ri
=
R3
Ra R Rc
=
R3
+
+
Chapter 4
Planar circuit circuits that can be drawn on a plane with no
crossing branches .
Nonplanar circuit circuits that not be drawn plane in that there are no branches
can on a such a
way crossing .
Terminology :
node :
point where two or more circuit elements join .
essential node
:
point where three or more circuit elements join .
path
:
a trace of adjoining basic elements with no elements included more than once .
branch path that connects two nodes
:
a .
· essential branch :
a path that connects two essential nodes without passing through an essential node .
loop : a path whose last node is the same as the starting node .
mesh a loop that does not enclose other
any loops
:
.
How equations ?
many
count number of essential nodes , ne
count number of essential branches be where current is unknown .
, ,
write ne-l equations by applying KCL to
any set of re-l nodes .
write be cre-ll equations by applying KVL around a set of be-(re-1) loops or meshes .
