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**Chapter 25 Electric Currents and Resistance**

HW7: Due Monday, March 30; Chap.24: Pb.32,Pb.35,Pb.59 Chap.25: Pb.19,Pb.25,Pb.31 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.

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**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.

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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.

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**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.

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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!

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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 +.

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**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:

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**25-3 Ohm’s Law: Resistance and Resistors**

The ratio of voltage to current is called the resistance:

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**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.

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**25-3 Ohm’s Law: Resistance and Resistors**

Conceptual Example 25-3: Current and potential. Current I enters a resistor R as shown. (a) Is the potential higher at point A or at point B? (b) Is the current greater at point A or at point B? Solution: a. Point A is at higher potential (current flows “downhill”). b. The current is the same – all the charge that flows past A also flows past B.

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**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.

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**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.

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**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.

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**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.

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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

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**25-4 Resistivity Example 25-5: Speaker wires.**

Suppose you want to connect your stereo to remote speakers. (a) If each wire must be 20 m long, what diameter copper wire should you use to keep the resistance less than 0.10 Ω per wire? (b) If the current to each speaker is 4.0 A, what is the potential difference, or voltage drop, across each wire? 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.

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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.

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**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? Solution: The resistance is proportional to the resistivity; use the temperature dependence of resistivity to find the temperature. T = 56.0 °C.

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

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**25-5 Electric Power The unit of power is the watt, W.**

For ohmic devices, we can make the substitutions:

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**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.

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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.

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**25-5 Electric Power Example 25-9: Electric heater.**

An electric heater draws a steady 15.0 A on a 120-V line. How much power does it require and how much does it cost per month (30 days) if it operates 3.0 h per day and the electric company charges 9.2 cents per kWh? Solution: P = IV = 1800 W W x 3.0 h/day x 30 days = 162 kWh. At 9.2 cents per kWh, this would cost $15.

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**25-6 Power in Household Circuits**

The wires used in homes to carry electricity have very low resistance. However, if the current is high enough, the power will increase and the wires can become hot enough to start a fire. To avoid this, we use fuses or circuit breakers, which disconnect when the current goes above a predetermined value.

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**25-6 Power in Household Circuits**

Fuses are one-use items – if they blow, the fuse is destroyed and must be replaced. Figure 25-19a. Fuses. When the current exceeds a certain value, the metallic ribbon melts and the circuit opens. Then the fuse must be replaced.

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**25-6 Power in Household Circuits**

Circuit breakers, which are now much more common in homes than they once were, are switches that will open if the current is too high; they can then be reset. Figure (b) One type of circuit breaker. The electric current passes through a bimetallic strip. When the current exceeds a safe level, the heating of the bimetallic strip causes the strip to bend so far to the left that the notch in the spring-loaded metal strip drops down over the end of the bimetallic strip; (c) the circuit then opens at the contact points (one is attached to the metal strip) and the outside switch is also flipped. As soon as the bimetallic strip cools down, it can be reset using the outside switch. Magnetic-type circuit breakers are discussed in Chapters 27 and 29.

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