1. Chapter 25 Electric Currents and Resistance
Chapter 25 opener. The glow of the thin wire filament of a light bulb is caused by the electric current passing through it. Electric energy is transformed to thermal energy (via collisions between moving electrons and atoms of the wire), which causes the wire’s temperature to become so high that it glows. Electric current and electric power in electric circuits are of basic importance in everyday life. We examine both dc and ac in this Chapter, and include the microscopic analysis of electric current.

2. 24-6 Molecular Description of Dielectrics
1. Dielectric is inserted +Q Eo -Q +Q -Q + - + -
2. Dielectric is polarized
3. Dielectric has internal Electric field + -
4. Electric Field is reduced by the dielectric constant, 
E weaker, V is smaller, but C is bigger

3. 24-6 Molecular Description of Dielectrics
This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential. This reorientation of the molecules results in an induced charge – there is no net charge on the dielectric, but the charge is asymmetrically distributed.
The magnitude of the induced charge depends on the dielectric constant:

4. 25-1 The Electric Battery
Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solution called an electrolyte.
This is a simple electric cell.
Figure Simple electric cell.

5. 25-1 The Electric Battery
A battery transforms chemical energy into electrical energy.
Chemical reactions within the cell create a potential difference between the terminals by slowly dissolving them. This potential difference can be maintained even if a current is kept flowing, until one or the other terminal is completely dissolved.

6. 25-1 The Electric Battery
Several cells connected together make a battery, although now we refer to a single cell as a battery as well.
Figure (a) Diagram of an ordinary dry cell (like a D-cell or AA). The cylindrical zinc cup is covered on the sides; its flat bottom is the negative terminal. (b) Two dry cells (AA type) connected in series. Note that the positive terminal of one cell pushes against the negative terminal of the other.

7. Unit of electric current: the ampere, A:
Electric current is the rate of flow of charge through a conductor:
The instantaneous current is given by:
Unit of electric current: the ampere, A:
1 A = 1 C/s.

8. 25-2 Electric Current
A complete circuit is one where current can flow all the way around. Note that the schematic drawing doesn’t look much like the physical circuit!
Figure (a) A simple electric circuit. (b) Schematic drawing of the same circuit, consisting of a battery, connecting wires (thick gray lines), and a lightbulb or other device.

9. 25-2 Electric Current
By convention, current is defined as flowing from + to -. Electrons actually flow in the opposite direction, but not all currents consist of electrons.
Figure Conventional current from + to - is equivalent to a negative electron flow from – to +.

10. 25-2 Electric Current Example 25-1: Current is flow of charge.
A steady current of 2.5 A exists in a wire for 4.0 min. (a) How much total charge passed by a given point in the circuit during those 4.0 min? (b) How many electrons would this be?
Solution: a. Charge = current x time; convert minutes to seconds. Q = 600 C.
b. Divide by electron charge: n = 3.8 x 1021 electrons.

11. 25-3 Ohm’s Law: Resistance and Resistors
Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends:

12. 25-3 Ohm’s Law: Resistance and Resistors
The ratio of voltage to current is called the resistance:
This is Ohm’s Law

13. Problem 5
5. (II) An electric clothes dryer has a heating element with a resistance of 8.6Ω (a) What is the current in the element when it is connected to 240 V? (b) How much charge passes through the element in 50 min? (Assume direct current.)

14. 25-2 Electric Current
Conceptual Example 25-2: How to connect a battery.
What is wrong with each of the schemes shown for lighting a flashlight bulb with a flashlight battery and a single wire?
Solution: a. Not a complete circuit.
b. Circuit does not include both terminals of battery (so no potential difference, and no current)
c. This will work. Just make sure the wire at the top touches only the bulb and not the battery!

15. 25-3 Ohm’s Law: Resistance and Resistors
In many conductors, the resistance is independent of the voltage; this relationship is called Ohm’s law (Ohmic Materials). Materials that do not follow Ohm’s law are called nonohmic.
Figure Graphs of current vs. voltage for (a) a metal conductor which obeys Ohm’s law, and (b) for a nonohmic device, in this case a semiconductor diode.
Unit of resistance: the ohm, Ω:
1 Ω = 1 V/A.

16. 25-3 Ohm’s Law: Resistance and Resistors
Example 25-4: Flashlight bulb resistance.
A small flashlight bulb draws 300 mA from its 1.5-V battery. (a) What is the resistance of the bulb? (b) If the battery becomes weak and the voltage drops to 1.2 V, how would the current change?
Figure Flashlight (Example 25–4). Note how the circuit is completed along the side strip.
a. R = V/I = 5.0 Ω.
b. Assuming the resistance stays the same, the current will drop to 240 mA.

17. Problem 9
9. (II) A 12-V battery causes a current of 0.60 A through a resistor. (a) What is its resistance, and (b) how many joules of energy does the battery lose in a minute?

18. 25-3 Ohm’s Law: Resistance and Resistors
Standard resistors are manufactured for use in electric circuits; they are color-coded to indicate their value and precision.
Figure The resistance value of a given resistor is written on the exterior, or may be given as a color code as shown above and in the Table: the first two colors represent the first two digits in the value of the resistance, the third color represents the power of ten that it must be multiplied by, and the fourth is the manufactured tolerance. For example, a resistor whose four colors are red, green, yellow, and silver has a resistance of 25 x 104 Ω = 250,000 Ω = 250 kΩ, plus or minus 10%. An alternate example of a simple code is a number such as 104, which means R = 1.0 x 104 Ω.

19. 25-3 Ohm’s Law: Resistance and Resistors
This is the standard resistor color code. Note that the colors from red to violet are in the order they appear in a rainbow.

20. 25-3 Ohm’s Law: Resistance and Resistors
Some clarifications:
Batteries maintain a (nearly) constant potential difference; the current varies.
Resistance is a property of a material or device.
Current is not a vector but it does have a direction.
Current and charge do not get used up. Whatever charge goes in one end of a circuit comes out the other end.

21. 25-4 Resistivity
The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area:
The constant ρ, the resistivity, is characteristic of the material. ρ is in Ω.m, A is the area

22. 25-4 Resistivity
Solution: a. R = ρl/A; you can solve this for A and then find the diameter. D = 2.1 mm.
b. V = IR = 0.40 V.

23. 25-4 Resistivity
For any given material, the resistivity increases with temperature:
Semiconductors are complex materials, and may have resistivities that decrease with temperature.0 and T0 are the resistivity and temperature at 0ºC or 20ºC.

24. 25-4 Resistivity Example 25-7: Resistance thermometer.
The variation in electrical resistance with temperature can be used to make precise temperature measurements. Platinum is commonly used since it is relatively free from corrosive effects and has a high melting point. Suppose at 20.0°C the resistance of a platinum resistance thermometer is Ω. When placed in a particular solution, the resistance is 187.4Ω. What is the temperature of this solution? ( α= °C-1)
Solution: The resistance is proportional to the resistivity; use the temperature dependence of resistivity to find the temperature. T = 56.0 °C.

25. Problem 23
23. (II) A length of aluminum wire is connected to a precision V power supply, and a current of A is precisely measured at 20.0°C. The wire is placed in a new environment of unknown temperature where the measured current is A. What is the unknown temperature? α= °C-1

26. 25-5 Electric Power
Power, as in kinematics, is the energy transformed by a device per unit time: or

27. 25-5 Electric Power The unit of power is the watt, W.
For ohmic devices, we can make the substitutions:

28. 25-5 Electric Power Example 25-8: Headlights.
Calculate the resistance of a 40-W automobile headlight designed for 12 V.
Solution: R = V2/P = 3.6 Ω.

29. 25-5 Electric Power
What you pay for on your electric bill is not power, but energy – the power consumption multiplied by the time.
We have been measuring energy in joules, but the electric company measures it in kilowatt-hours, kWh:
1 kWh = (1000 W)(3600 s) = 3.60 x 106 J.