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  5. Electro-techniques 143

Summary

Electro-techniques 143 Summary
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  • Course
  • Electro-techniques 143
  • Institution
  • Stellenbosch University (SUN)
  • Book
  • Electric Circuits

An in-depth, concise summary of circuit analysis techniques. Some concepts covered include voltage and current division, node-voltage and mesh-current methods, direct and indirect sources, Thévenin and Norton equivalent circuits, power transfer and optimisation, and superposition, among others.

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  • August 28, 2023
  • November 3, 2023
  • 27
  • 2023/2024
  • Summary

Subjects

  • electric circuit analysis

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  • Stellenbosch University (SUN)
  • Electro-techniques 143
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Content preview

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 .

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