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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.
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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: This is Ohm’s Law
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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.)
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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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25-3 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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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?
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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? ( Cu: ρ=1.68× 10-8Ωm) 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? ( 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.
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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
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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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