Chapters 16-1,2,3,5; 17-1; 18-2,3,4,5 Coulomb’s Law, Ohm’s Law, Power and Resistivity © 2014 Pearson Education, Inc.

A charged system or object can attract a neutral one by changing the distribution of charge in the neutral object Electric Charge © 2014 Pearson Education, Inc. Units of Charge: Coulombs (C) Charges produced by rubbing are typically around a microcoulomb: 1 µC = 10 −6 C

© 2014 Pearson Education, Inc. Smallest unit of charge is the electron at 1.6x C (on the equation sheet) and this is the elementary charge (e). Charge can only be lost or gained by this amount. You cannot lose or gain a fraction of an electron. So objects lose or gain charges in amounts of 1e, 2e, 3e, -500e, etc. Electron has a charge of –e and proton as having a charge of +e. The charges of electrons, neutrons and protons result from their quark compositions

Law of Conservation of Electric Charge © 2014 Pearson Education, Inc. Electric charge is conserved—the total charge of a system cannot change in any interaction (electrons and protons are conserved)

Coulomb’s Law The electric force between two point charges has to do with size of the chargesand distance between them. k = 9.0 × 10 9 N∙m 2 /C 2 © 2014 Pearson Education, Inc. Different on equation sheet

Direction of Electrical Force – along the line between the charges © 2014 Pearson Education, Inc. All contact forces (friction, normal, tension, etc) result from interatomic electric forces

Practice Problem © 2014 Pearson Education, Inc What is the magnitude and direction of the electric force on the electron of a hydrogen atom exerted by a single proton (Q 2 =+e) that is in the atom’s nucleus. The distance between them is 0.53x m.

Practice Problem © 2014 Pearson Education, Inc Two positive point charges Q 1 =50µC and Q 2 =1µC are separated by a distance r. Which is larger in magnitude, the force exerted by Q 1 on Q 2, or the force of Q 2 on Q 1 ? How is the direction related?

Electric Potential Energy and Potential Difference Electrostatic force is a conservative force, so there is electric potential energy, work can be done and electric PE can convert into KE © 2014 Pearson Education, Inc. PE in an electric field

Analogy between gravitational and electrical potential energy. Just as the more massive rock has more potential energy, so does the larger charge: © 2014 Pearson Education, Inc.

Electric potential (V) is the electric potential energy per unit charge. V=PE/q Just like with Ug = mgΔy, only a difference in electric potential is measureable. So we look at ∆V– this is the potential difference. Power sources maintain a nearly constant potential difference. Electric potential and potential difference are measured in Joules/Coulomb which is equal to Volts Voltage and potential difference are the same thing Batteries and power plants transform other types of energy into a potential difference Not on equation sheet

Electric Current Electric current is the rate of flow of charge through a conductor. It is Unit of electric current: the ampere, A. 1 A = 1 C/s © 2014 Pearson Education, Inc. Different on equation sheet

In order for current to flow, there must be a path from one terminal, through a closed circuit, and back to the other battery terminal. Circuit symbols:

Current is not a vector, but it has direction. By convention, current is defined as flowing from + to – (flow of positive charge). Electrons actually flow in the opposite direction. – blame the guys 200 years ago that didn’t know about electrons! Current and charge do not get used up (if it goes in one part of the circuit, it comes out the other) – law of conservation

Ohm’s Law Ohm’s Law: Resistance is a property for metal conductors. Ohm’s law doesn’t hold true under all conditions. (not really a true law – not sure why it hasn’t been demoted like Pluto) We use resistors to control the amount of current. Different on equation sheet

In many conductors, the resistance is independent of the voltage (death to Ohm’s Law). Materials that do not follow Ohm’s law are called nonohmic.

Practice Problem A steady current of 2.5 A exists in a wire for 4.0 min. (a) How much total charge passes by a given point in the circuit during those 4.0 min? (b) How many electrons would this be? Identify what, if anything, is wrong with each circuit below.

Practice Problem © 2014 Pearson Education, Inc A small flashlight bulb draws 300mA from a 1.5-volt battery. (a) What is the resistance of the bulb? (b) If the battery becomes weak and the voltage drops to 1.2-volts, how would the current change? Assume the bulb is approximately ohmic.

Practice Problem © 2014 Pearson Education, Inc Current enters a resistor as shown in this figure. A)Is the potential higher at point A or at point B? B)Is the current greater at Point A or Point B?

Resistivity The resistance of a wire is found using its length, cross sectional area and a property called resistivity (ρ ): The constant ρ, the resistivity, is characteristic of the material. Resistivity increases with temperature (perhaps atom movement is interfering with electron movement) – exception is in some semiconductors © 2014 Pearson Education, Inc.

18-4 Resistivity © 2014 Pearson Education, Inc.

Practice Problem © 2014 Pearson Education, Inc Suppose you want to connect your stereo to speakers that will be placed far away from the stereo. A)If each wire must be 20m long, what diameter wire do you need to keep the resistance less than 0.10Ω if the resistivity of copper is 1.68x10 -8 Ωm? B) If the current to each speaker is 4.0A, what is the voltage drop across each speaker?

Practice Problem © 2014 Pearson Education, Inc Suppose a wire could be stretched uniformly until it is twice its original length. What would happen to the resistance? Assume the amount of material, and therefore the volume, doesn’t change.

Electric Power – or Energy Dissipated over Time Power is the energy transformed by a device per unit time: For ohmic devices, we can derive these equations: © 2014 Pearson Education, Inc. Different on equation sheet Not on equation sheet

Direct and Alternating Current Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC). © 2014 Pearson Education, Inc.

Practice Problem © 2014 Pearson Education, Inc Calculate the resistance of a 40W car headlight designed for a 12V battery.

Chapter 19-1,2,3 DC Circuits © 2014 Pearson Education, Inc.

Resistors in Series A series connection has a single path. © 2014 Pearson Education, Inc. The current through each resistor is the same, but the voltage drop is different for each resistor. The sum of the voltage drops across the resistors equals the battery voltage. Not on equation sheet

Equivalent resistance (total resistance) – Different on equation sheet

Resistors in Parallel A parallel connection splits the current. Each resistor has a different current, but the voltage across each resistor is the same. © 2014 Pearson Education, Inc.

The total current is the sum of the currents across each resistor: The R eq is less than the R of any individual resistor. Different on equation sheet Not on equation sheet

Rules about Circuits Series Circuits: All resistors have the same I which is equal to the total I V is different for each resistor and they add to the total V Parallel Circuits: Each resistor has a different I that adds to the total I All resistors have the same V which is equal to the total V © 2014 Pearson Education, Inc.

Kirchhoff’s Rules Some circuits are much more complicated and need to be broken down or collapsed into different series and parallel parts. Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it (conservation of charge). © 2014 Pearson Education, Inc.

Loop rule: The sum of the changes in potential around a closed loop is zero (conservation of energy).

Solving Circuit Problems © 2014 Pearson Education, Inc. Follow up Questions 19-2 A) the lightbulbs in this figure are identical. Which configuration produces more light? B)Which way do you think the headlights of car are wired? 50Ω

Solving Circuit Problems – A bit harder now © 2014 Pearson Education, Inc.

Practice Problem [19-3] Two 100 Ω resistors are connected in parallel and in series to a 24.0 volt battery. What is the total resistance and the current in each circuit?

Practice Problem [19-4] How much current is drawn from the battery in the circuit?

Practice Problem [19-5] What is the current through the 500 Ω resistor?

Practice Problem © 2014 Pearson Education, Inc The circuit here has 3 identical bulbs. A)When the switch is closed, how will the brightness of bulbs A and B compare with that of C? B)What happens when the switch is opened? Answer in terms of brightness compared to before.

Practice Problem © 2014 Pearson Education, Inc. Exercise C. A 100W light bulb and 60W bulb are connected to a 120V power source in two different ways. In each case, which bulb glows more brightly? Why?