19/19/2015 Applied Physics Lecture 8  Electrodynamics Electric current current and drift speed resistance and Ohm’s law resistivity temperature variation of resistance electrical energy and power Chapter 17

29/19/2015 Lightning Review Last lecture: 1.Capacitance and capacitors Capacitors with dielectrics (C↑ if  ↑) Capacitors with dielectrics (C↑ if  ↑) 2.Current and resistance Electric current Electric current Current and drift speed Current and drift speed Review Problem: A parallel-plate capacitor is attached to a battery that maintains a constant potential difference V between the plates. While the battery is still connected, a glass slab is inserted so as to just fill the space between the plates. The stored energy a. increases b. decreases c. remains the same

39/19/ Current and Drift Speed Consider the current on a conductor of cross-sectional area A. A vdvd q vdtvdt

49/19/ Current and Drift Speed (2) Volume of an element of length  x is :  V = A  x. Let n be the number of carriers per unit of volume. The total number of carriers in  V is: n A  x. The charge in this volume is:  Q = (n A  x)q. Distance traveled at drift speed v d by carrier in time  t:  x = v d  t. Hence:  Q = (n A v d  t)q. The current through the conductor: I =  Q/  t = n A v d q.

59/19/ Current and Drift Speed (3) In an isolated conductor, charge carriers move randomly in all directions. When an external potential is applied across the conductor, it creates an electric field inside which produces a force on the electron. Electrons however still have quite a random path. As they travel through the material, electrons collide with other electrons, and nuclei, thereby losing or gaining energy. The work done by the field exceeds the loss by collisions. The electrons then tend to drift preferentially in one direction.

69/19/ Current and Drift Speed - Example Question: A copper wire of cross-sectional area 3.00x10 -6 m 2 carries a current of 10. A. Assuming that each copper atom contributes one free electron to the metal, find the drift speed of the electron in this wire. The density of copper is 8.95 g/cm 3.

79/19/2015 Question: A copper wire of cross-sectional area 3.00x10 -6 m 2 carries a current of 10 A. Assuming that each copper atom contributes one free electron to the metal, find the drift speed of the electron in this wire. The density of copper is 8.95 g/cm 3. Reasoning: We know: A = 3.00x10 -6 m 2 I = 10 A.  = 8.95 g/cm 3. q = 1.6 x C. n = 6.02x10 23 atom/mol x 8.95 g/cm 3 x ( 63.5 g/mol) -1 n = 8.48 x electrons/ cm 3.

89/19/2015 Question: A copper wire of cross-sectional area 3.00x10 -6 m 2 carries a current of 10 A. Assuming that each copper atom contributes one free electron to the metal, find the drift speed of the electron in this wire. The density of copper is 8.95 g/cm 3. Ingredients: A = 3.00x10 -6 m 2 ; I = 10 A.;  = 8.95 g/cm 3.; q = 1.6 x C. n = 8.48 x electrons/ cm 3.

99/19/ Current and Drift Speed - Comments Drift speeds are usually very small. Drift speed much smaller than the average speed between collisions. Electrons traveling at 2.46x10 -6 m/s would would take 68 min to travel 1m. Electrons traveling at 2.46x10 -6 m/s would would take 68 min to travel 1m. So why does light turn on so quickly when one flips a switch? The info (electric field) travels at roughly 10 8 m/s… The info (electric field) travels at roughly 10 8 m/s…

109/19/2015 Mini-quiz Consider a wire has a long conical shape. How does the velocity of the electrons vary along the wire? Every portion of the wire carries the same current: as the cross sectional area decreases, the drift velocity must increase to carry the same value of current. This is due to the electrical field lines being compressed into a smaller area, thereby increasing the strength of the electric field.

119/19/ Resistance and Ohm’s Law - Intro When a voltage (potential difference) is applied across the ends of a metallic conductor, the current is found to be proportional to the applied voltage. VV I

129/19/ Definition of Resistance In situations where the proportionality is exact, one can write. The proportionality constant R is called resistance of the conductor. The resistance is defined as the ratio.

139/19/ Resistance - Units In SI, resistance is expressed in volts per ampere. A special name is given: ohms (  ). Example: if a potential difference of 10 V applied across a conductor produces a 0.2 A current, then one concludes the conductors has a resistance of 10 V/0.2 a = 50 .

149/19/ Ohm’s Law Resistance in a conductor arises because of collisions between electrons and fixed charges within the material. In many materials, including most metals, the resistance is constant over a wide range of applied voltages. This is a statement of Ohm’s law. Georg Simon Ohm ( )

159/19/2015 I VV I VV Linear or Ohmic Material Non-Linear or Non-Ohmic Material Semiconductors e.g. devices called diodes Most metals, ceramics

169/19/2015 Ohm’s Law R understood to be independent of  V.

179/19/2015 Definition: resistor Resistor: a conductor that provides a specified resistance in an electric circuit. I V = IR E +-

189/19/2015 Example: Resistance of a Steam Iron All household electric devices are required to have a specified resistance (as well as many other characteristics…). Consider that the plate of a certain steam iron states the iron carries a current of 7.40 A when connected to a 120 V source. What is the resistance of the steam iron?

199/19/ Resistivity - Intro Electrons moving inside a conductor subject to an external potential constantly collide with atoms of the conductor. They lose energy and are repeated re-accelerated by the electric field produced by the external potential. The collision process is equivalent to an internal friction. This is the origin of a material’s resistance.

209/19/2015 The resistance of an ohmic conductor is proportional to the its length, l, and inversely proportional to the cross section area, A, of the conductor Resistivity - Definition The constant of proportionality  is called the resistivity of the material.

219/19/ Resistivity - Remarks Every material has a characteristic resistivity that depends on its electronic structure, and the temperature. Good conductors have low resistivity. Insulators have high resistivity. Analogy to the flow of water through a pipe.

229/19/ Resistivity - Units Resistance expressed in Ohms, Length in meter. Area are m 2, Resistivity thus has units of  m.

239/19/2015 Material Resistivity (10 -8  m) Material Resistivity (10 -8  m) Silver1.61Bismuth106.8 Copper1.70Plutonium141.4 Gold2.20Graphite1375 Aluminum2.65Germanium4.6x10 7 Pure Silicon 3.5Diamond2.7x10 9 Calcium3.91Deionized water 1.8x10 13 Sodium4.75Iodine1.3x10 15 Tungsten5.3Phosphorus1x10 17 Brass7.0Quartz1x10 21 Uranium30.0Alumina1x10 22 Mercury98.4Sulfur2x10 23 Resistivity of various materials

249/19/2015 Mini-quiz Why do old light bulbs give less light than when new? Answer: The filament of a light bulb, made of tungsten, is kept at high temperature when the light bulb is on. It tends to evaporate, I.e. to become thinner, thus decreasing in radius, and cross sectional area. Its resistance increases with time. The current going though the filament then decreases with time – and so does its luminosity. Tungsten atoms evaporate off the filament and end up on the inner surface of the bulb. Over time, the glass becomes less transparent and therefore less luminous.

259/19/ Resistivity - Example (a) Calculate the resistance per unit length of a 22-gauge nichrome wire of radius m. Cross section: Resistivity (Table): 1.5 x 10   m. Resistance/unit length:

269/19/ Resistivity - Example (b) If a potential difference of 10.0 V is maintained across a 1.0-m length of the nichrome wire, what is the current?

279/19/ Temperature Variation of Resistance - Intro The resistivity of a metal depends on many (environmental) factors. The most important factor is the temperature. For most metals, the resistivity increases with increasing temperature. The increased resistivity arises because of larger friction caused by the more violent motion of the atoms of the metal.

289/19/2015 For most metals, resistivity increases approx. linearly with temperature.  is the resistivity at temperature T (measured in Celsius).   is the reference resistivity at the reference temperature T  ( usually taken to be 20 o C).  is a parameter called temperature coefficient of resistivity. For a conductor with fixed cross section. For a conductor with fixed cross section.  T Metallic Conductor  T Superconductor

299/19/ Temperature Variation of Resistance - Example Platinum Resistance Thermometer A resistance thermometer, which measures temperature by measuring the change in the resistance of a conductor, is made of platinum and has a resistance of 50.0  at 20 o C. When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 . Find the melting point of Indium. Solution: Using  =3.92x10 -3 ( o C) -1 from table 17.1.

309/19/2015 Platinum Resistance Thermometer A resistance thermometer, which measures temperature by measuring the change in the resistance of a conductor, is made of platinum and has a resistance of 50.0  at 20 o C. When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 . Find the melting point of Indium. Solution: Using  =3.92x10 -3 ( o C) -1 from table R o =50.0 . T o =20 o C. R=76.8 .