Formula Sheets: Network Basics & Basic Laws | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

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Net w ork Theory: Net w ork Basics & Basic La ws
F orm ula Sheet for Electrical GA TE
Net w ork Basics
• Net w ork Elemen ts :
– P assiv e Elemen ts : Resistor (R , ? ), Inductor (L , H ), Capacitor (C , F ).
– A ctiv e Elemen ts : V oltage source (V , V ), Curren t source (I , A ).
• Ohm’s La w : Relationship b et w een v oltage, curren t, and resistance.
V =IR
• P o w er in a Circuit : P o w er dissipated or supplied.
P =VI =I
2
R=
V
2
R
(Units: W )
• Resistance in Series and P arallel :
R
series
=R
1
+R
2
+ · · ·+R
n
1
R
parallel
=
1
R
1
+
1
R
2
+ · · ·+
1
R
n
Kirc hhoff ’s La ws
• Kirc hhoff ’s Curren t La w (K CL) : Sum of curren ts en tering a no de equals sum of
curren ts lea ving.
?
I
in
=
?
I
out
• Kirc hhoff ’s V oltage La w (KVL) : Sum of v oltage drops around a closed lo op is
zero.
?
V =0
Net w ork Analysis
• V oltage Divider R ule : V oltage across a resistor in series.
V
x
=V
total
·
R
x
R
1
+R
2
+ · · ·+R
n
• Curren t Divider R ule : Curren t through a resistor in parallel.
I
x
=I
total
·
R
eq
R
x
, where
1
R
eq
=
?
1
R
i
( excluding R
x
)
• Star-Delta T ransformation :
R
?
=
R
1
R
2
+R
2
R
3
+R
3
R
1
R
i
( for R
i
opp o site to R
?
)
R
star
=
R
a
R
b
R
a
+R
b
+R
c
( for R
a
,R
b
,R
c
in delta)
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Net w ork Theory: Net w ork Basics & Basic La ws
F orm ula Sheet for Electrical GA TE
Net w ork Basics
• Net w ork Elemen ts :
– P assiv e Elemen ts : Resistor (R , ? ), Inductor (L , H ), Capacitor (C , F ).
– A ctiv e Elemen ts : V oltage source (V , V ), Curren t source (I , A ).
• Ohm’s La w : Relationship b et w een v oltage, curren t, and resistance.
V =IR
• P o w er in a Circuit : P o w er dissipated or supplied.
P =VI =I
2
R=
V
2
R
(Units: W )
• Resistance in Series and P arallel :
R
series
=R
1
+R
2
+ · · ·+R
n
1
R
parallel
=
1
R
1
+
1
R
2
+ · · ·+
1
R
n
Kirc hhoff ’s La ws
• Kirc hhoff ’s Curren t La w (K CL) : Sum of curren ts en tering a no de equals sum of
curren ts lea ving.
?
I
in
=
?
I
out
• Kirc hhoff ’s V oltage La w (KVL) : Sum of v oltage drops around a closed lo op is
zero.
?
V =0
Net w ork Analysis
• V oltage Divider R ule : V oltage across a resistor in series.
V
x
=V
total
·
R
x
R
1
+R
2
+ · · ·+R
n
• Curren t Divider R ule : Curren t through a resistor in parallel.
I
x
=I
total
·
R
eq
R
x
, where
1
R
eq
=
?
1
R
i
( excluding R
x
)
• Star-Delta T ransformation :
R
?
=
R
1
R
2
+R
2
R
3
+R
3
R
1
R
i
( for R
i
opp o site to R
?
)
R
star
=
R
a
R
b
R
a
+R
b
+R
c
( for R
a
,R
b
,R
c
in delta)
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Energy Storage Elemen ts
• Inductor V oltage and Curren t :
V
L
=L
dI
dt
, I
L
(t)=
1
L
?
V
L
(t)dt
• Capacitor V oltage and Curren t :
I
C
=C
dV
dt
, V
C
(t)=
1
C
?
I
C
(t)dt
• Energy Stored :
E
L
=
1
2
LI
2
, E
C
=
1
2
CV
2
Key Notes
• Use SI units: V oltage (V ), Curren t (A ), Resistance (? ), P o w er (W ).
• F or K CL/KVL, assign consisten t curren t directions and lo op p olarities.
• Chec k for dep enden t sources in GA TE problems (e.g., V CCS, CCVS).
• F or transien t analysis, initial conditions for L and C are critical.
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