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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 iC dt i(t) C u(t) t qt i t dt qt0 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 ) 0.5 104 [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 wt 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 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 [email protected] by E-mail. To describe to main idea and answer some questions.