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Lecture 10-1 ©2008 by W.H. Freeman and Company Lecture 10-2 C Capacitor Examples C 2C C C1 C2 C C C C/2 1 0 A / 2 d A 2 0 1 d 2 2 0 A / 2 d C C ?C ?=2/3 1 1 1 d / 4 3d / 4 C C1 C2 0 A 0 A d 1 3 1 0 A 4 4 Lecture 10-3 READING QUIZ 1 An electric toaster (resister) uses 2000 watts when the it is connected to a 100 volt potential difference. What is the resistance R (Ω) of the toaster? A| 10 Ω B| 5 Ω C| 15 Ω D| 20 Ω E| 12 Ω Lecture 10-4 DOCCAM 2 DEMO 5B-01 OHMS LAW BOARD Lecture 10-5 DOCCAM 2 DEMO 5B-O3 VOLTAGE PARADOX Lecture 10-6 Electric Current Current = charges in motion q dq Magnitude I lim x 0 t dt rate at which net positive charges move across a cross sectional surface I J dA Units: [I] = C/s = A (ampere) J = current density (vector) in A/m² Current is a scalar, signed quantity, whose sign corresponds to the direction of motion of net positive charges by convention A Lecture 10-7 Microscopic View of Electric Current in Conductor All charges move with some velocity ve A random motion with high speeds (O(106)m/s) but with a drift in a certain direction on average if E is present Why random motion? • thermal energy • scattering off each other, defects, ions, … Drift velocity vd is orders of magnitudes less than the actual velocity of charges. Lecture 10-8 Current and Drift Velocity in Conductor Drift velocity vd is orders of magnitudes less than the actual velocity of charges. I nAvd q I vd nAq where n =carrier density or J nqv d ( E ) if ohmic Lecture 10-9 Ohm’s Law Summary Current-Potential (I-V) characteristic of a device may or may not obey Ohm’s Law: I V (J E) or V = IR with R constant V V Resistance R I A (ohms) tungsten wire gas in fluorescent tube diode Lecture 10-10 Resistance and Resitivity for Ohmic Material J E E J (= I/A if current density is uniform) resistivity I L V EL L I A A A L R (in) Ohms Ω resistance Lecture 10-11 Resistance Resistance (definition) V R I R I V constant R L R A Ohm’s Law Lecture 10-12 Warm up quiz 2 There are 2x1014 electrons entering a resistor in10 seconds. What is the current through the resistor? a) 2.0 μA b) 1.6 mA c) 3.2 nA d) 1.6 A e) 3.2 μA Note: e = 1.6x10-19 C R I V Lecture 10-13 Temperature Dependence of Resistivity 0 1 (T T0 ) • Usually T0 is 293K (room temp.) • Usually α > 0 (ρ increases as T ) Material ρ0 (Ωm) α (K-1) Ag 1.6x10-8 3.8x10-3 Cu 1.7x10-8 3.9x10-3 Si 6.4x102 -7.5x10-2 glass 1010 ~ 1014 sulfur 1015 Copper Lecture 10-14 Electric Current and Joule Heating electron gas • Free electrons in a conductor gains kinetic energy due to an externally applied E. • Scattering from the atomic ions of the metal and other electrons quickly leads to a steady state with a constant current I. Transfers energy to the atoms of the solid (to vibrate), i.e., Joule heating. Mean drift of electrons, i.e., current Lecture 10-15 Energy in Electric Circuits • Steady current means a constant amount of charge ΔQ flows past any given cross section during time Δt, where I= ΔQ / Δt. Energy lost by ΔQ is V U Q (Va Vb ) I t V => heat So, Power dissipation = rate of decrease of U = dU P IV I 2 R V 2 / R dt Lecture 10-16 EMF – Electromotive Force • An EMF device is a charge pump that can maintain a potential difference across two terminals by doing work on the charges when necessary. Examples: battery, fuel cell, electric generator, solar cell, fuel cell, thermopile, … • Converts energy (chemical, mechanical, solar, thermal, …) into electrical energy. Within the EMF device, positive charges are lifted from lower to higher potential. If work dW is required to lift charge dq, dW dq Volt EMF Lecture 10-17 Energy Conservation A circuit consists of an ideal battery (B) with emf ε, a resistor R, and two connecting wires of negligible resistance. Energy conservation • Ideal battery: no internal energy dissipation • Real battery: internal energy dissipation exists Work done by battery is equal to energy dissipated in resistor dW i 2 Rdt or i dt i 2 R dt iR EMF ε = terminal voltage V dW > i2Rdt then εi > iR=V Lecture 10-18 DOCCAM 2 DEMO 5B-02 TERMINAL VOLTAGE ON A BATTERY Lecture 10-19 Resistors in Series The current through devices in series is always the same. i R1 R2 i i Req ε ε iR1 iR2 0 iReq 0 Req ( R1 R2 ) For multiple resistors in series: Req R1 R2 R3 ... Lecture 10-20 Internal Resistance of a Battery Life story (ups and downs) of a charge load i r iR 0 internal resistance i Rr terminal voltage , Vb Va ir R Rr Lecture 10-21 Lecture 10:30 quiz 3 September 22, 20ll There are 1014 electrons entering in 10 seconds a resistor which has a potential drop of 3.2μV. What is the resistance of the resistor? a) 4.0 Ω b) 1.0 mΩ c) 2.0 Ω d) 3.0 μΩ e) 2.0 kΩ Note: e = 1.6x10-19 C R I V Lecture 10-22 Lecture 11:30 quiz 3 September 22, 2011 There are 1014 electrons entering a resistor of resistance 1.0 Ω in 10 seconds. What is the potential drop across the resistor? a) 3.2 mV b) 8.0 V c) 2.5 V d) 1.6 μV e) 1.6 mV Note: e = 1.6x10-19 C R I V Lecture 10-23 Lecture 11:30 quiz 3 February 10, 2011 The potential drop is 6.4mV across a resistor of resistance 1.0Ω. How many electrons enter the wire in 5 seconds? a)3.2×1014 b)8.0×1015 c)2.5×1012 d)2.0×1017 e)1.6×1019 Note: e = 1.6x10-19 C R I V