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Chapter 3Inductance and Capacitance
2008.9
Electrical Engineering and Electronics II Electrical Engineering and Electronics II
Scott
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.
•Main Contents
•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
背极电容单指向会议话筒
油浸纸电容式套管耦合电容
超级电容公交车电源
电容性话筒
空调电容高压电容补偿箱
3.1 CAPACITANCE
Cvq
dt
dvCi
0
0
tqdttitqt
t
0
0
1tvdtti
Ctv
t
t
•Stored charge in terms of voltage
•Capacitance acts as open circuits for steady dc voltages.
Cu(t)
i(t)
Passive reference configuration
3.1 CAPACITANCE
•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.
)]10cos(1[105.0)( 44 ttq )]10cos(1[500)( 4 ttu
•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).
•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.
dt
tdvtcvtitvtp
)()()()()(
)(2
1)()()()( 2
)(
00
tcvtdvtcvdttptwtvt
t
The energy:
C
tqtvtqtw
2
)()()(
2
1)(
2
Energy flows in capacitor
Energy flows out of capacitor
•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.
1 2 3 1 2 3
1 2 3
du du du dui i i i C C C C
dt dt dt dtC C C C
•Capacitors in parallel are combined like resistances in series.
3.2 Capacitances in Series and Parallel•Capacitances in Parallel
321
321
321
1111
1
111
CCC
C
idtC
idtC
idtC
idtC
uuuu
Capacitors in series are combined like resistances in parallel.
•Capacitances in series
3.2 Capacitances in Series and Parallel
3.3 Physical Characteristics of Capacitors
AC
dA WL
mF 1085.8 120
ε 0 r
r Relative dielectric constant,相对介电常数
0 Vaccum dielectric constant,真空介电常数
•Capacitance of the Parallel-Plate Capacitor
•Practical Capacitors
•Real capacitors have maximum voltage ratings.
•How to describe the charging or discharging process of capacitance?
3.4 Inductance
螺线管线圈 铁心线圈
铁氧体线圈
贴片电感标准电感棒形电感 环形电感
新型电感镇流器 电子变压器
3.4 Inductance
单相变压器 试验变压器 三相变压器
心式变压器的内部结构
3.4 Inductance
电磁调速异步电动机
三相自动扶梯用异步电动机 变频调速异步电动机
三相异步电动机
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
•Voltage is proportional to the time rate of change of current
Passive reference configuration
3.4 Inductance
•Current in terms of voltage
dt
diLtv
0
0
1tidttv
Lti
t
t
tLiLididttptwt
t
t
t
2
2
1)(
0 0
Power and Energy for a capacitor
•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
变压器
非磁性棒
铁心
原（一次）绕组
副（二次）绕组
3.7 Mutual Inductance
Page 137 Practical application 3.1
Electronic Photo Flash To finish the group table, 4~5 persons in every
group and select a leader. To write down the main idea of Practical
application 3.1 in Word document and send it to suntao@cqu.edu.cn by E-mail.
To describe to main idea and answer some questions.
Teamwork 2