Lecture Electric circuit theory: Basic laws - Nguyễn Công Phương

Nguyễn Công Phương

Electric Circuit Theory
Basic Laws


Contents
I. Basic Elements Of Electrical Circuits
II. Basic Laws
III. Electrical Circuit Analysis
IV. Circuit Theorems
V. Active Circuits
VI. Capacitor And Inductor
VII. First Order Circuits
VIII.Second Order Circuits
IX. Sinusoidal Steady State Analysis
X. AC Power Analysis
XI. Three-phase Circuits
XII. Magnetically Coupled Circuits
XIII.Frequency Response
XIV.The Laplace Transform
XV. Two-port Networks
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Basic Laws
1.
2.
3.

4.
5.

Ohm’s law
Nodes, branches, and loops
Kirchhoff’s laws
Series subcircuits
Parallel subcircuits

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3


Ohm’s law (1)
i
+

v

R
v
v = Ri

Slope = R
–

i

→ p(t) = Ri2(t)

p(t) = v(t)i(t)

1
i = v = Gv
R
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4


Ohm’s law (2)

i

v

+

Slope = R

–

i

i

Req

v

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+

–

v

5


Ohm’s law (3)
i(t)

vs = 0

i(t)

i(t)

R=0

+ –

+

v

–

+

v

–

+

v

–

Short circuit

i(t)
+

is = 0
v

i(t)
–

+

R=∞
v

i(t)

–

+

v

–

Open circuit
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6


Basic Laws
1.
2.
3.
4.
5.

Ohm’s law
Nodes, branches, and loops
Kirchhoff’s laws
Series subcircuits
Parallel subcircuits

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Nodes, branches, and loops (1)
A branch represents a single element
R3

R1
R2
+

E1

+

–

R4

J

E2 –

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Nodes, branches, and loops (2)
A node is the point of connection between two or more branches
a

R1

R3

b

c

R2
+

E1

R4

+

–

d

J

E2 –
e

f

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Nodes, branches, and loops (3)
A loop is any closed path in a circuit
R3

R1
R2
+

E1

R4

+

–

J

E2 –

b=l+n–1
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10

Basic Laws
1.
2.
3.
4.
5.

Ohm’s law
Nodes, branches, and loops
Kirchhoff’s laws
Series subcircuits
Parallel subcircuits

Basic Laws - sites.google.com/site/ncpdhbkhn

11


Kirchhoff’s current law (1)
N

∑ in = 0

(KCL)

n =1

i1

i2

i1

i4

i3

i4

i2

i3

i1 − i2 + i3 − i4 = 0
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12


Kirchhoff’s current law (2)

+
–

12 V

2A

1A

2Ω

4Ω
1A

4A
8Ω

3A
1Ω

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13


Kirchhoff’s voltage law (1)
N

∑ un = 0

(KVL)

n =1

vb

R1

+ –

+ v1 –
+
–

va

– v3 +

+
v2
–

R2

−va + v1 + vb + v2 + v3 = 0

R3
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Kirchhoff’s voltage law (2)

+
–

12 V

2A

1A

+ 4V –

+4V –

1A

+
8V
–

4A

+
4V

3A

–

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15


Basic Laws
1.
2.

3.
4.
5.

Ohm’s law
Nodes, branches, and loops
Kirchhoff’s laws
Series subcircuits
Parallel subcircuits

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Series subcircuits (1)

i

i
+

a

–

+ –

E1

E2

+

a
+

v

+ –

v
b

–

–

Eeq = E1 + E2

b

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Series subcircuits (2)

i

i
+

+

a
J1

v

–

a

J2
Jeq = J1 = J2

v
b

–

b

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Series subcircuits (3)
i
+

a

R1
+ v1 –

i

R2
+

+ v2 –

v

v
–

a

b

–

Req = R1 + R2
b

v = v1 + v2

→ v = R1i + R2i = ( R1 + R2 )i = Req i
v1 = R1i
v
i=
R1 + R2

R1
→ v1 =
v
R1 + R2

R2
v2 =
v
R1 + R2

Rk
vk =
v
R1 + ... + Rk + ... + RN
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Series subcircuits (4)

i

i
+

a

+ –
E

v

–

+

a

J
Jeq = J

v
b

–

b

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20

Basic Laws
1.
2.
3.
4.
5.

Ohm’s law
Nodes, branches, and loops
Kirchhoff’s laws
Series subcircuits
Parallel subcircuits

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Parallel subcircuits (1)

i

i
+
v
–

+

a
J1
b

J2

a

v
–

Jeq = J1 + J2
b

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Parallel subcircuits (2)

i

i
a

+

–

–

b

E2

+

E1

+

v
–

+

a

v
–

–

+

Eeq = E1 = E2

b

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Parallel subcircuits (3)
i

i
+

a

v
–

+
R1

b

R2

i1

i2

a

Req =

1

v

1
1
+
R1 R2

–

R1 R2
=
R1 + R2

b

1
v
v
1 
1
i = i1 + i2 = +
= ( G1 + G2 ) v =  +  v = Geq v =
v
R1 R2
Req
 R1 R2 

1
R1 R2
→ Req =
=
1
1
R1 + R2
+
R1 R2
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Parallel subcircuits (4)
i
+

a

v
–

R1

i2

b

i = ( G1 + G2 ) v

i1 = G1v

R2

i1

R2
i1 =
i
R1 + R2

G1
→ i1 =
i
G1 + G2
G2
i2 =
i
G1 + G2

Gk
ik =
i
G1 + ... + Gk + ... + GN

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