Batteries. Current and Resistance. Battery. Circuits. Drift Speed 6/1/2016. Chapter 18

Transcription

1 Batteries Current and Resistance Chapter 18 Battery Circuits Batteries provide Chemical Electricity Electrons bunch up or have the potential to flow from the negative end Electrons can t flow in an isolated battery - e e e e Chemical Reaction that produces electrons + Chemical Reaction that absorbs electrons Drift Speed Electrons do not flow through wires like pipes Electric field gives direction to the random motion of electrons. (v D = drift speed) 0.05 mm/s About 5 ½ hours to travel one meter (coin waterfall at Chuck-E-Cheese) About a year to go 1 mile 1

2 Conventional Current Flows positive to negative Opposite of electron flow (electron current) Current (I) Current Net amount of charge per unit time 1 coulomb/second = 1Ampere I = DQ Dt I = dq dt A steady current of 2.5 A flows through a wire for 4.0 min. How much charge passed through any point in the circuit? I = DQ Dt DQ = IDt DQ = (2.5 A)(240 s) = 600 C How many electrons would this be? 1 electron = 1.60 X C 600 C 1 electron = 3.8 X electrons 1.60 X C The current through a wire is 1.90 A. a. Calculate how long it would take 2280 C of charge to flow (20 minutes) b. Calculate the amount of charge that flows each hour (6840 C) c. How many electrons flowed in one hour? The charge on an electron is 1.60 X C. (4.28 X electrons) 2

3 In one minute, C of charge flows through a wire in a car engine. a. Calculate the current (12.0 A) b. Calculate how many electrons flowed in one minute. The charge on an electron is 1.60 X C. (4.50 X electrons) In two minutes, 6.75 X electrons flowed through a flashlight circuit. a. Calculate how many coulombs flowed through the circuit (1080 C) b. Calculate the current (9.00 A) The total amount of charge that enters a wire is given by the expression Q = 2t 2 t, where t is in seconds. a. Determine the expression for the current in the wire. b. Calculate the current at 2 seconds and at 4 seconds. c. Determine the expression for the current using Q = 1.5sint as the expression. Ohm s Law V = IR DV = IR V = Voltage (V) I = Current (A) R = Resistance (Ohms, W) (only works for metal conductors, not semiconductors (nonohmic)) Resistors Color coded to determine resistance Devices that heat have high resistance (light bulbs, electric stoves, toasters) A small flashlight bulb draws 300 ma from a 1.5 V battery. a. Calculate the resistance of the bulb (5.0 W) b. If the voltage dropped to 1.2 V and the resistance stayed at 5.0 W, what current would flow. (240 ma) 3

4 Resistivity R = rl A R = Resistance L = Length (longer wire, greater resistance) A = Area (wider wire, less resistance) r = Resistivity of the material What is the resistance of a 2.00mm diameter, 10.0 meter copper wire? A speaker wire must be 20.0 m long and have a resistance of less than W per wire. a. What diameter copper wire should be used? (2.06 mm) b. What is the voltage drop across each wire at a current of 4.00 A? (0.40 V) R = W or 53.5 m W A wire of length L is stretched to twice its normal length. a. Calculate the new cross sectional area (assume the volume does not change (A new =1/2A) b. Calculate the new resistance (R new = 4R) The resistance of nichrome wire in a toaster is 9.8 Ω. The wire is 220 cm long and the resistivity is 110x10-8 Ω m. Calculate the diameter of the wire. (0.56 mm) 4

5 A wire of uniform cross-section has a resistance of R. What would be the resistance of a similar wire, made of the same material, but twice as long and of twice the diameter? Resistance and Temperature Metals Resistance increases with temp. Atoms more disorderly Interferes with flow of electrons Semiconductors Resistance sometimes decreases with temperature Some electrons become excited and able to flow Superconductivity The resistance of a platinum resistor at 20 o C is W. Calculate the resistance at 56.0 o C. Superconductivity resistance of a material becomes zero No loss of current over a wire Generally near absolute zero Record as of 2015 is 203 K Maglev trains Electric Power Watt 1 Watt = 1 Joule 1 second P = I 2 R P = IV P = V 2 R 5

6 Calculate the resistance of a 40-W auto headlight that operates at 12 V. P = I 2 R (3.6 W) An electric heater draws 15.0 A on a 120-V line. How much power does it use? P = I 2 R V = IR so R = V/I P = I 2 V I P = IV = (15 A)(120V) = 1800 W or 1.8 kw A lightning bolt can transfer 10 9 J of energy at a potential difference of 5 X 10 7 V over 0.20 s. What is the charge transferred? V = PE/Q Q = E/V = 10 9 J/ 5 X 10 7 V = 20 C What is the current? I = DQ/Dt I = 20 C/0.2 s = 100 A What is the power? P = I 2 R V = IR so R = V/I P = I 2 V I P = IV = (100 A)(5 X 10 7 V ) = 5 X 10 9 W Household Electricity Kilowatt-hour You do not pay for power, you pay for energy 1 kwh = (1000 J)(3600 s) = 3.60 X 10 6 J 1s How much does it cost to run an 1800 W dryer for 30 days if it operates 3.0 h per day and the electric company charges 10.5 cents per kwh? Hours = 30 days X 3.0 h/day = 90 h Cost = (1.80 kw)(90 h)($0.105/kwh) = $17 6

7 Household Electricity Circuit breakers prevent overloading (too much current per wire) Metal melts or bimetallic strip expands Household Electricity: Ex 1 Determine the total current drawn by all of the appliances shown. P = IV I = P/V I light = 100W/120 V = 0.8 A I light = 100W/120 V = 0.8 A I heater = 1800W/120 V = 15 A I stereo = 350W/120 V = 2.9 A I hair = 1200W/120 V = 10.0 A You leave a 60 W lightbulb on outside your house for 12 hours a day for an entire month (30 days). How many kilowatt hours will you be charged for? I total = 0.8A A + 2.9A A = 28.7 A This would blow the 20 A fuse You decide to turn your computer (75 W) off every night. Assume that it is off for 9 hours every night for 30 days. How many kilowatthours did you save? Suppose you are charged for 3000 kwh for a given month. How many Joules of energy did you use that month? (Hint: Start from the power formula) 7

8 Jump Starting a Car POSITIVE TO POSITIVE (or your battery could explode) DC vs AC DC Electrons flow constantly Electrons flow in only one direction Batteries AC Electrons flow in short burst Electrons switch directions (120 times a second) House current DC vs AC DC vs AC DC = Direct current Electrons flow constantly Electrons only flow in one direction (negative to positive) Batteries provide DC current DC vs AC AC = Alternating current Electrons switch directions Pulsed current Home electricity More efficient for power transmission over large distances USA uses 60 Hertz (60 cycles per second), many other countries use 50 Hz I = I o sin2pft AC Current I o = Peak current (highest possible) V rms = root-mean square voltage I rms = root-mean square current 8

9 In the United States, the rms voltage is 120 V. Calculate the peak voltage. (170 V) In Europe, the rms voltage is 240 V. Calculate the peak voltage. (340 V) A hair dryer has a power of 1000-W and is connected to a 120 V line (rms). a. Calculate the rms current that runs through the dryer. (8.33 A) b. Calculate the resistance of the dryer. c. Calculate the power through the dryer if you plug it into a 240 V line in Europe. A stereo reciever has an average power of W and a resistance of 8.00 W a. Calculate the rms voltage. [28.3 V] b. Calculate the rms current. [3.534 A] c. Calculate peak voltage and peak current. [40.0 V, 5 A] d. Calculate the rms voltage if you turn down the speaker so it is only 1.00 W. [2.82 V] An AC source has an rms voltage of V. The resistance of the circuit 20.0 W a. Calculate rms current [10.0 A] b. Calculate peak current [14.1 A] c. Calculate the average power [2000 W] d. Calculate the maximum power [4000 W] An AC source has an rms Voltage of 17.0 V and is connected to a circuit with 265 W of resistance. a. Calculate peak voltage [24.0 V] b. Calculate the rms current [64.1 ma] c. Calculate the average power [1.09 W] d. Calculate the maximum power. [2.18 W] 9

10 The total charge that passes through a wire is given by the following function: Q = (3t 2 + 2t)C. a. Sketch a quick graph for the interval 0-5 seconds. b. Determine the expression for current in the wire at any given time. c. Calculate the current at 2 seconds. The current in a wire at a given time is given by the function I = 5t 2. a. Determine the expression for the charge. b. Determine the total charge that has passed through the wire from 0 to 5 seconds The current in a wire at a given time is given by the function I = 5e -t/4ms a. Sketch a graph of I from 0 to 8 ms b. Determine the expression for the charge. c. Determine the total charge that has passed through the wire from 0 to 8 ms A 3.0 V flashlight has a resistance of 15.0 ohms. The voltage decreases according to the following graph. a. Determine the formula for the current that passes through the wire in that time interval. b. Determine the formula for the total charge moved by the batteries. c. Calculate the total charge that moved in those 5.0 hours days X s N/C X m 10. a) 7.43 X 10-6 m/s b) 2.1 X s 12. a) 1.73 X 10 7 A/m 2 b) 5.3 X s ma ma 18. a) 6.3 X 10 5 A/m 2 b) 6.5 X 10-5 m/s A X 10-8 Wm 26. a) 1.64 X 10-3 N/C b) 1.10 X 10-5 m/s 30. a) 1.00 b) X 10-8 Wm 34. a) 3.0 W, 30 m b) 1.0 A W W V/m X 10 5 C mm 10

11 54.a) , 12.6, 17.3, 19.0, 19.6, 19.9 b) (10A)e -t/2 c) 10.0 A at t=0 s d) 10, 6.07, 3.68, 1.35, 0.50, 0.18, a) 4.2 X 10 5 A b) 1.80 X 10 5 V/m c) Current decreases d) 1.2 X 10-5 J 11

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