普通物理 General Physics 26 - Ohm's Law 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

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Outline 26-1 What Is Physics? 26-2 Electric Current 26-3 Current Density 26-4 Resistance and Resistivity 26-5 Ohm’s Law 26-6 A Microscopic View of Ohm’s Law 26-7 Power in Electric Circuits 26-8 Semiconductors 26-9 Superconductors 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 26-1 What Is Physics? In this and the next chapter, we discuss the physics of electric currents —that is, charges in motion. 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 26-2 Electric Current A B i + q Conductor i - q Conductor Current = rate at which charge flows Current SI Unit: C/s known as the “Ampere”. 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-1 Water flows through a garden hose at a volume flow rate dV/dt of 450 cm3/s. What is the current of negative charge? 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-1 Solutions: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 26-3 Current Density i + q Conductor A i - q Conductor A SI unit for J: A/m2 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 26-3 Current Density Drift velocity 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 23-2 (a) The current density in a cylindrical wire of radius R = 2.0 mm is uniform across a cross section of the wire and is J = 2.0 × 105 A/m2.What is the current through the outer portion of the wire between radial distances R/2 and R? 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 23-2 (b) Suppose, instead, that the current density through a cross section varies with radial distance r as J = ar2, in which a = 3.0 × 1011 A/m4 and r is in meters. What now is the current through the same outer portion of the wire? 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 23-2 (a) Solutions: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 23-2 (b) Solutions: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-3 What is the drift speed of the conduction electrons in a copper wire with radius r = 900 μm when it has a uniform current i = 17 mA? Assume that each copper atom contributes one conduction electron to the current and that the current density is uniform across the wire’s cross section. 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-3 Solutions: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

26-4 Resistance and Resistivity + - i V If we apply a voltage V across a conductor a current i will flow through the conductor. We defined the conductor resistance as the ratio. R V/i = the ohm (symbolΩ) 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

26-4 Resistance and Resistivity + - i V SI unit: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

26-4 Resistance and Resistivity Conductivity: Resistance-resistivity relation: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

26-4 Resistance and Resistivity 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-4 A rectangular block of iron has dimensions 1.2 cm × 1.2 cm × 15 cm. A potential difference is to be applied to the block between parallel sides and in such a way that those sides are equipotential surfaces. 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-4 What is the resistance of the block if the two parallel sides are (1) the square ends (with dimensions 1.2 cm × 1.2 cm) and (2) two rectangular sides (with dimensions 1.2 cm × 15 cm)? 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-4 Solutions: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-5 Figure shows a person and a cow, each a radial distance D = 60.0 m from the point where lightning of current I = 100 kA strikes the ground. The current spreads through the ground uniformly over a Hemisphere centered on the strike point. 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-5 The person’s feet are separated by radial distance ∆rper = 0.50 m; the cow’s front and rear hooves are separated by radial distance ∆rcow = 1.50 m. The resistivity of the ground is ρgr = 100 Ω‧m. The resistance both across the person, between left and right feet, and across the cow, between front and rear hooves, is R = 4.00 kΩ. 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-5 (a) What is the current ip through the person? (b) What is the current ic through the cow? 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-5 Solutions: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-5 Solutions: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 26-5 Ohm’s Law 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

26-6 A Microscopic View of Ohm’s Law 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-6 (a) What is the mean free time τ between collisions for the conduction electrons in copper? (b) The mean free path λ of the conduction electrons in a conductor is the average distance traveled by an electron between collisions. What is λ for the conduction electrons in copper, assuming that their effective speed veff is 1.6 × 106 m/s? 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-6 Solutions: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

26-7 Power in Electric Circuits SI unit for P: V‧A It is known as the “Watt” (symbol W). For Ohmic conductors: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-7 You are given a length of uniform heating wire made of a nickel–chromium–iron alloy called Nichrome; it has a resistance R of 72 Ω. At what rate is energy dissipated in each of the following situations? (1) A potential difference of 120 V is applied across the full length of the wire. (2) The wire is cut in half, and a potential difference of 120 V is applied across the length of each half. 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 Example 26-7 Solutions: 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 26-8 Semiconductors Property Unit Copper Silicon Type of material Metal Semiconduct Charge carrier density m3 8.49×1028 1×1016 Resistivity Ω·m 1.69×108 2.5×103 Temperature coefficient of resistivity K－1 4.3×103 －70×103 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 26-9 Superconductors 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 26-9 Superconductors In 1911, Dutch physicist Kamerlingh Onnes discovered that the resistivity of mercury absolutely disappears at temperatures below about 4 K. This phenomenon of superconductivity is of vast potential importance in technology because it means that charge can flow through a superconducting conductor without losing its energy to thermal energy. 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授

普通物理講義-26/國立彰化師範大學物理系/郭艷光教授 End of chapter 26! 2018/12/3 普通物理講義-26/國立彰化師範大學物理系/郭艷光教授