1B-week8

1B-week8 - Physics 1B Eighth Week W. Gekelman Current and...

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Unformatted text preview: Physics 1B Eighth Week W. Gekelman Current and Resistors G. Ohm 1787-1854 Friday, May 21, 2010 A simple circuit Battery + - i i Resistor i Friday, May 21, 2010 Ohms’ Law Length of resistor Area of resistor Resistance Electrical Resistivity (depends upon the material) Friday, May 21, 2010 Definition of electrical current Coulombs Current (Amperes) Flow of charge through a wire Seconds Friday, May 21, 2010 J = current density = Amps/m2 J is a vector , I is not! A Electron path Resistor Friday, May 21, 2010 I Assume E ┴ A You can have a current only if there is a potential difference Friday, May 21, 2010 Power energy / time= joule/sec=Watt 1 foot-pound/hour 1 kiloCalorie/hour 1 kiloCaloris/min Typical lightbulb 1 horsepower 1 hairdryer 1 gallon gas/hour 1 gallon gas/minute Pulsed Yag laser 1 nuclear reactor Lightning strike 1 million barrels oil/day NIF laser US electricity (average) consumption 1.16 Watt 1.16 W 69.77 W 100 W 745.7 W 1 kW (k = 103) 39 kW 2.5 MW (M=106) 150 MW 3 GW (G = 109) 5 GW 73 GW 360 TW (T=1012) 3.41 TW Friday, May 21, 2010 Energy Something with enormous power may not be on for very long (i.e.) the NIF laser ON= 10-9 sec E= 3.6X1014 X 5X10-9 = 1.8X106 Joules Energy of 1 ton high explosives = 4.2X109 J Hydrogen Bomb (1 MT) = 4.2X1015 J Friday, May 21, 2010 What formula units Amps Ohms Amps/m2 comments Flow of charge Electrical analog of friction I, current dQ/dt, R resistance Current density microscopic Energy/time Power Watt Friday, May 21, 2010 Series Resistors in Series and Parallel R1 a i b R2 c Vac = Vab +Vbc iReq=iR1+iR2 Req = R1 +R2 Friday, May 21, 2010 Resistors in Series and Parallel i i2 i1 R1 R2 i1 i2 i Friday, May 21, 2010 25 Friday, May 21, 2010 26 Friday, May 21, 2010 27 Friday, May 21, 2010 28 Friday, May 21, 2010 What is resistance between a and b ? 30 Friday, May 21, 2010 Rules for circuit analysis 1) Current is conserved at each node i1=i2+i3 i1 i3 i2 R i 2) Voltage drop across a resistor in direction of the current is –iR (why???) Friday, May 21, 2010 Rules for circuit analysis 3) Voltage drop around any closed loop is zero i1 R1 E1 E2 R3 i3 i2 R2 i4 Friday, May 21, 2010 Rules for circuit analysis 3) Voltage drop around any closed loop is zero i1 R1 E1 E2 R3 i3 i2 R2 i4 Friday, May 21, 2010 S has been closed a long time , find voltages and currents before and after opened R a i1 b S Left loop: currents E r i2 R R i3 Right Loop answer c Friday, May 21, 2010 Given the circuit below: Use the circuit analysis laws to find the current in each loop (and then the voltage drop across each resistor) These are in series These 2 Ohm and 3 Ohm are in parallel with the series combination Friday, May 21, 2010 6Ω 2Ω Series combo These are all in parallel Friday, May 21, 2010 a b Loop a: 4.0I2 +6.0I1 -12 = 0 Loop b: +4.0I3- 6.0 -6.0I1+12.0 = 0 Current at point A: I1+I3 = i2 Friday, May 21, 2010 Loop a: 4.0i2+6.0i1 -12 = 0 Loop b: +4.0i3-6.0-6.0i1+12.0 = 0 Current at point A: i1+i3 = i2 Loop b + current: 10I1-4I2 = 6 loop a 6I1+4i2=12 Add these 16I1 = 18 I1 = 1.125 A Substitute into –Loop a I2 = 1.31 A 6(1.125)+4I2 = 12 and i3 = i2-i1 = 0.19A Power Dissipated Friday, May 21, 2010 ...
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