Lecture Electric circuit theory: Capacitor and inductor - Nguyễn Công Phương

Nguyễn Công Phương

Electric Circuit Theory
Capacitor & Inductor


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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Capacitor & Inductor
1. Capacitor
2. Inductor
3. The Dc Steady State

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Capacitor (1)

q

i, q C
+

v

q = Cv

dq
i=
dt

Slope = C
–

v

dv
→i =C
dt
1 t

v(t ) = ∫ i (α ) dα
C −∞

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Capacitor (2)
i, q
+

v
–

i, q
i1, q1

i2, q2

C1

C2

+

v
–

Ceq = C1 + C2

i = i1 + i2
dv
i1 = C1
dv
dv
dv
dv
= (C1 + C2 ) = Ceq
dt → i = C1 + C2
dt
dt
dt
dt
dv
i2 = C2
dt
Ceq = C1 + C2 + ... + Cn
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i, q
+

Capacitor (3)

v1
+

v2
C2

–

+

+

C1

v

i, q

–

–

v
–

v = v1 + v2

Ceq =

1
1
1

+
C1 C2

C1C2
=
C1 + C2

1 t
1 t
1 t
v1 (t ) = ∫ i (α ) dα
→ v = ∫ i(α ) dα +
i (α ) dα
C1 −∞
∫
−∞
−∞
C1
C2
1 t
v2 (t ) =
i(α )dα
1
1  t
1 t
∫
−∞
C2
=  +  ∫ i (α ) dα =
i(α )dα

∫
−∞
−∞
Ceq
 C1 C2 
1
1
1
1
= +
+ ... +
Ceq C1 C2
Cn
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Inductor (1)
i
+

λ

L
v

λ = Li
dλ
v=

dt

Slope = L
–

i

di
→v= L
dt

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Inductor (2)
i
+

v
–

+

v1
L1

i

–
+

L2

v2
–

v = v1 + v2
di
v1 = L1
dt
di
v2 = L2
dt

+

v

Leq = L1 + L2

–

di
di
di
di
→ v = L1 + L2 = ( L1 + L2 ) = Leq
dt

dt
dt
dt

Leq = L1 + L2 + ... + Ln
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Inductor (3)
i

i

+

i1

v
L1

–

i2
L2

+

Leq =

v
–

=

i = i1 + i2
1 t
i1 (t ) = ∫ v (α )dα
L1 −∞

1
i2 (t ) =
L2

∫

t

−∞

v(α )dα

1
1 1
+
L1 L2
L1 L2
L1 + L2

1 t
1 t
→ i = ∫ v(α )dα + ∫ v (α )dα
L1 −∞
L1 −∞
1 1  t
1
=  +  ∫ v (α )dα =
Leq
 L1 L2  −∞

∫

t

−∞

v(α )dα

1
1 1
1
= + + ... +
Leq L1 L2
Ln
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Capacitor & Inductor
1. Capacitor
2. Inductor
3. The Dc Steady State

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The Dc Steady State (1)
i

L

i

v

+

–

v=0

+

–

di

v=L
dt → v = 0
i = const

i, q C
+

v
dv
i=C
dt
v = const

i=0
–

+

v

–

→i=0
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The Dc Steady State (2)
Ex. 1

R1

Solve the circuit?

R3

+

R2

–

E

E
i1 = i2 = iL =
R1 + R2

i3 = iC = 0

L

i1
i2

+

iL

uL

–

–

E

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R3

i3

+

+

E
= R2i2 = R2
R1 + R2

R2

uC
–

R1

vL = 0

vC = vR 2

C

iC

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