1. 5.2 The Source-Free Responses of RC and RL Circuits 5.4 Step Response of an RC Circuit 5.1 Capacitors and Inductors 5.3 Singularity Functions 5.5 Complete Response of an RL Circuit Chapter 5 First-order Circuits 一阶电路

2. In this chapter,we shall examine two types of simple circuits: a circuit comprising a resistor and capacitor and a circuit comprising a resistor and an inductor. These are called RC and RL circuits. We carry out the analysis of RC and RL circuits by applying Kirchhoff’s laws, and producing differential equations. The differential equations resulting from analyzing RC and RL circuits are of the first order. Hence,the circuits are collectively known as first-order circuits.

3. Ⅰ. Capacitors 电容 A capacitor consists of two conducting plates separated by an insulator. 绝缘体 Insulator 绝缘体 Conducting Plates 导电极板 Measured in Farads(F) 法拉 Capacitance 电容（值） A capacitor properties: 特性 5.1 Capacitors and Inductors 电容和电感 vcvc Memory 记忆 Storage element 储能元件 Open circuit to dc The voltage on a capacitor cannot change abruptly

4. Ⅱ. Inductors 电感 Measured in henrys(H) 亨利 Inductance 电感（值） An inductor properties: An inductor consists of a coil of conducting wire. length, l Core material μ Cross-sectional area, A Number of turns, N Memory 记忆 Storage element 储能元件 Short circuit to dc The current through an inductor cannot change abruptly.

5. 5.2 The Source-Free Response of RC and RL Circuits 一阶电路的零输入响应 t >0: Ⅰ.The Source-free RC Circuit Time constant 时间常数

6. If there are many resistors in the circuit: R eq is the equivalent resistance of resistors. The key to working with a source-free RC circuit is finding: 1.The initial voltage v(0 + ) across the capacitor. 2. The time constant .

8. Ⅱ. The Source-Free RL Circuit i L (0 + ) : The initial current through the inductor Time constant 时间常数

9. Example 5.1 The switch in the circuit has been closed for a long time. At t=0, the switch is opened. Calculate i(t) for t>0. Solution: Hence Thus,

10. 1. The step function 阶跃函数 u(t) 1 0t 5.3 Singularity Functions 奇异函数 The delayed step function: 延迟阶跃函数 u(t-t0)u(t-t0) t0t0 1 0t The general step function: A 0 t t0t0

11. Replace a switch by the step function:

12. 2. The impulse function 冲激函数  (t) (1) 0t The delayed impulse function: tt0t0 0  (t-t 0 ) (1)(1)

13. 5.4 Step Response of an RC Circuit 阶跃响应 The complete response 全响应 The temporary response 暂态响应 V s ： The steady-state response 稳态响应 (The forced response ) 强制响应 (The natural response ) 自由响应

14. 0 vc(t)vc(t) V0V0 VSVS t V0<VSV0<VS vc(t)vc(t) VSVS 0 t V0V0 V0>VsV0>Vs

15. Source-free response 零输入响应 Zero-state response 零状态响应 Forced response 强制响应 Natural response 自由响应 The complete response 全响应

16. 1. The initial capacitor voltage v(0 + ). 2. The final capacitor voltage v(  ). 3. The time constant . The complete response of an RC circuit requires three things: If the switch changes position at time t=t 0,so the equation is

17. 5.5 Complete Response of an RL Circuit Three-factor method 三要素法 1. The initial value f(0 + ). 2. The final value f(  ). 3. The time constant .

18. Example 5.2 The circuit is in steady-state, switch S is closed at t=0. Calculate when. Solution:

19. Example 5.3 The circuit is in steady-state, switch S moves from position 1 to 2 at t=0. Calculate when Solution:

20. 部分电路图和内容参考了： 电路基础（第 3 版），清华大学出版社 电路（第 5 版），高等教育出版社 特此感谢！