Transcript for a capacitance or inductance given the voltage

Electrical Engineering and Electronics II
Chapter 3
Inductance and Capacitance
Scott
2008.9
•Main Contents
1. Find the current (voltage) for a capacitance or
inductance given the voltage (current) as a
function of time.
2. Compute the capacitances of parallel-plate
capacitors.
3. Compute the stored energies in capacitances
or inductances.
4. Find the voltages across mutually coupled
inductances in terms of the currents.
•Passive element

Resistances—energy-consumption elements

energy—storage elements
----inductance and capacitance
•Capacitors is the circuit property that accounts
for energy stored in electric fields.
•Inductors is the circuit property that accounts for
energy stored in magnetic fields.
3.1 CAPACITANCE
C: unit-F, μF, pF
3.1 CAPACITANCE
背极电容单指
向会议话筒
耦合电容
高压电容补偿箱
电容性话筒
油浸纸电容式套管
超级电容公交车电源
空调电容
3.1 CAPACITANCE
•Stored charge in terms of voltage
Passive reference
configuration
q  Cv
dv
iC
dt
i(t)
C
u(t)
t
qt    i t dt  qt0 
t0
t
1
v t    i t dt  v t0 
C t0
•Capacitance acts as open circuits for steady dc voltages.
•Determining current for a capacitance given voltage
•Example 3.1 Suppose the voltage v(t) is applied to a 1μF
capacitance. Plot the stored charge and the current through the
capacitance versus time.
•Example 3.2 Suppose the current i(t) is applied to a 0.1μF capacitance. The
initial charge on it is q(t)=0. Plot the i(t), q(t) and v(t).
q(t )  0.5 104 [1  cos(104 t )]
u(t )  500[1  cos(104 t )]
•Stored energy

The power delivered to a circuit element is the
product of the current and the voltage provided that
the references have the passive configuration.
dv(t )
p (t )  v(t )i (t )  cv (t )
dt

The energy:
1 2
w(t )   p(t )dt   cv(t )dv(t )  cv (t )
t
0
2
1
q 2 (t )
w(t )  q(t )v(t ) 
2
2C
t
0
v(t )
•Example 3.3 The voltage is applied to a 10μF capacitance. Plot the voltage,
power, and stored energy to scale versus time for t between 0 and 5s.
Energy flows in
capacitor
Energy flows out
of capacitor
3.2 Capacitances in Series and Parallel
•Capacitances in Parallel
du
du
du
du
i  i1  i2  i3  C1
 C2
 C3
C
dt
dt
dt
dt
 C  C1  C2  C3
•Capacitors in parallel are combined like resistances in series.
3.2 Capacitances in Series and Parallel
•Capacitances in series
u  u1  u2  u3
1
1
1
  idt 
idt 
idt


C1
C2
C3
1
  idt
C
C 
1
1
1
1


C1 C2 C3
Capacitors in series are combined like resistances in parallel.
3.3 Physical Characteristics of Capacitors
•Capacitance of the Parallel-Plate Capacitor
C
A
d
A  WL
ε0  8.85 10
12
Fm
 0 Vaccum dielectric constant,真空介电常数
 r Relative dielectric constant,相对介电常数
   r 0
•Practical Capacitors
•Real capacitors have maximum voltage ratings.
•How to describe the charging or
discharging process of capacitance?
3.4 Inductance
铁氧体线圈
螺线管线圈
铁心线圈
3.4 Inductance
棒形电感
新型电感镇流器
标准电感
贴片电感
电子变压器
环形电感
3.4 Inductance
单相变压器
心式变压器的内部结构
三相变压器
试验变压器
3.4 Inductance
三相异步电动机
三相自动扶梯用异步电动机
电磁调速异步电动机
变频调速异步电动机
3.4 Inductance
同步电动机
交流伺服电动机
BC系列反应式步进电动机
3.4 Inductance
交流接触器
3.4 Inductance
Passive reference
configuration
•Voltage is proportional to the time rate of change of current
•Current in terms of voltage
di
v t   L
dt
t
1
i t    v t dt  i t0 
L t0
Power and Energy for a capacitor
t
t
1 2
wt    p(t )dt   Lidi  Li t 
2
t0
t0
•Example 3.6 The current flows through a 5H inductance. Plot the voltage,
power, and stored energy to scale versus time for t between 0 and 5s.
•Example 3.7 We have a switch that close at t=0, connecting a 10 V
source to a 2-H inductance. Find the current as a function of time.
•How to describe the charging or
discharging process of Inductance?
3.5 Inductances in Series and Parallel
•Exercise 3.10 Find the equivalent
inductance for each of the circuits.
3.7 Mutual Inductance
Self Inductance, 自感
3.7 Mutual Inductance
非磁性棒
副（二次）绕组
原（一次）绕组
铁心
变压器
Teamwork 2




Page 137 Practical application 3.1
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