Chapter 27: Current and Resistance Reading assignment: Chapter 27 Homework 27.1, due Wednesday, Oct. 19: OQ1, 5, 14 Homework 27.2, due Friday, Oct. 21: OQ3, OQ6, 15, 21, 25, 26, 31, 33, 39, 44, 48, 53 Begin our study of charges in motion --> electric current  Electrodynamics Invention of battery, Alessandro Volta, 1800 --> production of steady electric current Electrical current and circuits are omnipresent in today’s technological world Electric current, Ohm’s law, resistance, resistivity, electric power

Batteries There is a potential difference (voltage) between the terminals of a battery: Series connection: Voltages add up in a series connection. The voltage between the ends of three 1.5 V batteries connected in series is 3x1.5V = 4.5V. Symbol of battery in a circuit: + -

Electric current Symbol for battery When a continuous conducting path is connected between the terminals of a battery, we have an electrical circuit. When such a circuit is formed, charge can flow through the wires of the circuit, from one terminal of the battery to the other. A flow of charge, such as this is called an electrical current. The electrical current, I, in a wire is defined as the amount of charge that passes through it per unit time. Instantaneous current DQ is the amount of charge that passes through the conductor at any location during time interval Dt. The direction of current is the direction in which positive charges flow Unit of electrical current is Ampere (1A) (Coulomb/second).

How to connect a battery What’s wrong with each of the schemes shown in the Figure for lighting a flashlight with a flashlight battery and a single wire? (a) (b) (c) - There is no loop for the current to flow around. There is loop to and from the light bulb, but there is no potential difference. Nothing wrong here. The bulb will light up. i-clicker: Current flow of charge. A steady current of 2.5 A flows in a wire for 4.0 minutes (Be careful to use SI units). How much charge passes through any point in the circuit? 0 C C) 600 C 10 C D) 1000 C 2) How many electrons would this be?

Ohm’s Law Or: Ohm’s Law Resistance: Unit of resistance: 1 Ohm (1 W) To produce an electrical current I in a wire, a difference in potential V is required (set up by a battery, power supply or outlet). Ohm’s law: The current in the wire is proportional to the potential difference applied to its ends: The amount of current flowing in a wire for a given voltage depends on the resistance of the wire, R. The higher the resistance the less current will flow for a given voltage. Or: Ohm’s Law Georg Simon Ohm 1789 – 1854 Resistance: Unit of resistance: 1 Ohm (1 W)

White board example Ohm’s law. Flashbulb light resistance. A small light bulb draws 300 mA from its 1.5 V battery What is the resistance of the light bulb? If the voltage dropped to 1.2 V how would the current change?

Resistors All electric devices offer resistance to the flow of current (filaments of light bulbs or electric heaters) Resistors are used to control the amount of current. They have a resistance ranging from less than on Ohm to millions of Ohms. Symbol in a circuit is How to read the code (four band code): First find the tolerance band, it will typically be gold ( 5%) and sometimes silver (10%). Starting from the other end, identify the first band - write down the number associated with that color. Now 'read' the next color Now read the third or 'multiplier' band If the resistor has one more band past the tolerance band it is a quality band. Read the number as the '% failure rate per 1000 hour' This is rated assuming full wattage being applied to the resistors.

Resistivity and Resistance of a wire The resistance of a wire is proportional to its length L and inversely proportional to its cross-sectional area A. The proportionality constant r is called the resistivity. It depends on the material and has units of W·m. There is a huge range of values across different materials. Typically metals (the best is silver r = 1.6x10-8 W·m) have a very low resistivity (are good conductors). Insulators have a very high resistivity (glass: 109 – 1010 W·m).

Effect of temperature on resistivity and resistance Typically (but not always!) the resistivity (and thus the resistance) of metals increases with increasing temperature. At higher temperatures the atoms are moving more rapidly and thus interfere with the flow of the electrons. RT and R0 are resistance at temperature T and reference temperature T0 (usually 20°C) a is the temperature coefficient of resistivity (see Table 27-2) a can be negative for semiconductors, i.e. resistance decreases with increasing temperature! Why?

Semi-conductors Toughened glass insulator on high voltage power line http://www.parsmaghareh.com/En/index.htm

White board example Resistance thermometer. The variation in electrical resistance with temperature can be used to make precise temperature measurements. Suppose at 20oC the resistance of a platinum resistance thermometer is 164.2 W. When placed in a particular solution, the resistance is 187.4 W. What is the temperature of this solution?

Electric power Electric energy is useful, because it can be easily transformed into other forms of energy (heat, light, mechanical). Electrons lose all their energy (potential) as they travel through the circuit from one terminal of the battery to the other terminal Remember: electric potential energy: DUel = QDV Power is measured in Watt By using Ohm’s law, V = IR, the power in a resistor can be written as:

Black board example Electric heater. An electric heater draws 15.0 A on a 120V line (regular household outlet; this is alternating current (AC), but all equations are still valid). How much power does it us? How much does it cost to operate it for 90 hours if the electric company charges 10.5 cents per kWh? (Assume steady current flow in one direction)

Black board example Lightning bolt. In a typical lightning event, 109 J of energy are transferred across a potential difference of 5 x 107 V during a time interval of 0.2 seconds. Use this information to estimate the total amount of charge transferred, the current and the average power over the 0.2 seconds.

Microscopic model of current and Ohm’s law again I … current n … density of charge carriers q … charge per carrier vd … drift velocity A … cross-sectional area Ohm’s law J… current density, I/A s… conductivity, s = 1/r; r… resistivity, (material constant) E … electric field

Review Definition of current: Ohm’s Law (common def.): Resistance of a wire: Temp. dependence of resistivity r, Resistance, R: Microscopic definition of current, I, and Ohm’s law