普通物理 General Physics 27 - Circuit Theory 郭艷光 Yen-Kuang Kuo 國立彰化師大物理系暨光電科技研究所 電子郵件：ykuo@cc.ncue.edu.tw 網頁：http://ykuo.ncue.edu.tw

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Outline 27-1 What Is Physics? 27-2 “Pumping” Charges 27-3 Work, Energy, and Emf 27-4 Calculating the Current in a Single-Loop Circuit 27-5 Other Single-Loop Circuits 27-6 Potential Difference Between Two Points 27-7 Multiloop Circuits 27-8 The Ammeter and the Voltmeter 27-9 RC Circuits 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-1 What Is Physics? In this chapter, we cover the physics of electric circuits that are combinations of resistors and batteries and capacitors. We restrict our discussion to circuits through which charge flows in one direction, which are called either direct-current circuits or DC circuits. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-2 “Pumping” Charges In order to create a current through a resistor, a potential difference must be created across its terminals. A device that can maintain a potential difference between two terminals is called a “seat of an emf” or an “emf device”. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-3 Work, Energy, and Emf V i Ideal emf device Pump High (+) reservoir Low (-) reservoir V i Real emf device 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-3 Work, Energy, and Emf 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

27-4 Calculating the Current in a Single-Loop Circuit Loop Rule: The algerbraic sum of the changes in potential encountered in a complete traversal of any loop in a circuit is equal to zero. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

27-4 Calculating the Current in a Single-Loop Circuit Resistance Rule: For a move through a resistance in the direction of the current, the change in the potential: For a move through a resistance in the direction opposite to that of the current, the change in the potential: R i Motion R i Motion 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

27-4 Calculating the Current in a Single-Loop Circuit EMF Rule: For a move through an ideal emf device in the direction of the emf arrow, the change in the potential: For a move through an ideal emf device in a direction opposite to that of the emf arrow, the change in the potential: Motion + - Motion + - 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

27-5 Other Single-Loop Circuits 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

27-5 Other Single-Loop Circuits Resistances in series: When a potential difference V is applied across resistances connected in series, the resistances have identical currents i. The sum of the potential differences across the resistances is equal to the applied potential difference V. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

27-6 Potential Difference Between Two Points Left path: Right path: Note: The values we get from the two paths are the same. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-1 The emfs and resistances in the circuit of Figure have the following values: ε1=4.4 V, ε2=2.1 V, r1=2.3Ω, r2=1.8Ω, R=5.5Ω. (a) What is the current i in the circuit? (b) What is the potential difference between the terminals of battery 1 in Figure? 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-1 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-1 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-7 Multiloop Circuits i1+i3=i2 KJR: The sum of the currents entering any junction is equal to the sum of the current leaving the junction. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-7 Multiloop Circuits Resistances in Parallel: When a potential difference V is applied across resistances connected in parallel, the resistances all have that same potential difference V. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-7 Multiloop Circuits 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-2 Figure shows a multiloop circuit containing one ideal battery and four resistances with the following values: R1=20Ω, R2=20Ω,ε=12 V, R3= 30Ω, R4=8.0Ω. (a) What is the current through the battery? (b) What is the current i2 through R2? (c) What is the current i3 through R3? 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-2 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-2 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-3 Figure shows a circuit whose elements have the following values: ε1=3.0 V,ε2=6.0 V R1=2.0Ω, R2=4.0Ω The three batteries are ideal batteries. Find the magnitude and direction of the current in each of the three branches. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-3 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-4 Electric fish are able to generate current with biological cells called electroplaques, which are physiological emf devices. The electroplaques in the type of electric fish known as a South American eel are arranged in 140 rows, each row stretching horizontally along the body and each containing 5000 electroplaques. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-4 The arrangement is suggested in Figure; each electroplaque has an emfεof 0.15 V and an internal resistance r of 0.25Ω. The water surrounding the eel completes a circuit between the two ends of the electroplaque array, one end at the animal’s head and the other near its tail. (a) If the water surrounding the eel has resistance Rw =800Ω, how much current can the eel produce in the water? (b) How much current irow travels through each row of Figure? 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-4 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

27-8 The Ammeter and the Voltmeter 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-9 RC Circuits + - i Charging of a capacitor i =?? 加分!! 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-9 RC Circuits 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-9 RC Circuits + - i Discharging of a capacitor q t qo O 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-5 As a car rolls along pavement, electrons move from the pavement first onto the tires and then onto the car body. The car stores this excess charge and the associated electric potential energy as if the car body were one plate of a capacitor and the pavement were the other plate .When the car stops, it discharges its excess charge and energy through the tires, just as a capacitor can discharge through a resistor. 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 Example 27-5 If a conducting object comes within a few centimeters of the car before the car is discharged, the remaining energy can be suddenly transferred to a spark between the car and the object. Suppose the conducting object is a fuel dispenser. The spark will not ignite the fuel and cause a fire if the spark energy is less than the critical value Ufire = 50 mJ. When the car of Fig. a stops at time t= 0, the car– ground potential difference is V0 = 30 kV. The car–ground capacitance is C = 500 pF, and the resistance of each tire is Rtire = 100 GΩ. How much time does the car take to discharge through the tires to drop below the critical value Ufire? 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-9 RC Circuits 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 27-9 RC Circuits 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授

普通物理教材-27，國立彰化師範大學物理系/郭艷光教授 End of chapter 27! 2018/11/27 普通物理教材-27，國立彰化師範大學物理系/郭艷光教授