* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Presentation_12
Thermal runaway wikipedia , lookup
Negative resistance wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Power MOSFET wikipedia , lookup
Integrated circuit wikipedia , lookup
Surge protector wikipedia , lookup
Nanofluidic circuitry wikipedia , lookup
Flexible electronics wikipedia , lookup
Galvanometer wikipedia , lookup
Operational amplifier wikipedia , lookup
Wilson current mirror wikipedia , lookup
Electromigration wikipedia , lookup
Opto-isolator wikipedia , lookup
Two-port network wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
RLC circuit wikipedia , lookup
Rectiverter wikipedia , lookup
Current source wikipedia , lookup
Network analysis (electrical circuits) wikipedia , lookup
WARNING: Exam is Thursday, 7:30 – 9 pm Room 54-100 Review Sessions: Me: Tuesday Imran: Wednesday In class: Thursday Office Hours: Brian F.: Tuesday Brian P.: Wednesday 4-6 pm 6-120 8-10 pm 4-270 12-2 pm; 2-4 pm 8-10 pm 6-402 4-6 pm 6-106 Please email me questions P12- 1 Class 12: Outline Hour 1: DC Circuits Hour 2: Expt. 6: Simple Circuits P12- 2 Last Time: Capacitors & Dielectrics P12- 3 Capacitors & Dielectrics Capacitance To calculate: 1) Put on arbitrary ±Q 2) Calculate E 3) Calculate V Q C V Energy 2 E Q2 1 1 2 U Q V C V uE d 3r o d 3r 2 2C 2 2 Dielectrics qin E dA S 0 CFilled with Dielectric C0 P12- This Time: DC Circuits P12- Examples of Circuits P12- 6 Current: Flow Of Charge Average current Iav: Charge Q flowing across area A in time t Q I av t Instantaneous current: differential limit of Iav dQ I dt Units of Current: Coulombs/second = Ampere P12- 7 Direction of The Current Direction of current is direction of flow of pos. charge or, opposite direction of flow of negative charge P12- 8 Current Density J J: current/unit area I J Iˆ A Î points in direction of current I J nˆ dA J d A S S P12- 9 Why Does Current Flow? If an electric field is set up in a conductor, charge will move (making a current in direction of E) Note that when current is flowing, the conductor is not an equipotential surface (and Einside ≠ 0)! P12-10 Microscopic Picture Drift speed is velocity forced by applied electric field in the presence of collisions. It is typically 4x10-5 m/sec, or 0.04 mm/second! To go one meter at this speed takes about 10 hours! How Can This Be? P12- 11 Conductivity and Resistivity Ability of current to flow depends on density of charges & rate of scattering Two quantities summarize this: s: conductivity r: resistivity P12-12 Microscopic Ohm’s Law E rJ r or J sE 1 s r and s depend only on the microscopic properties of the material, not on its shape P12-13 Demonstrations: Temperature Effects on r P12-14 PRS Questions: Resistance? P12-15 Why Does Current Flow? Instead of thinking of Electric Field, think of potential difference across the conductor P12-16 Ohm’s Law What is relationship between V and current? b V Vb Va E d s E a E V / J r r I J A r V I IR A P12-17 Ohm’s Law V IR R r A R has units of Ohms (W) = Volts/Amp P12-18 Examples of Circuits P12-19 Wires in Circuits Wires in circuit diagrams are “perfect conductors.” They are thus equipotentials, and can be stretched, shrunk... as long as you don’t change the potentials! Must maintain all equipotential surfaces! P12-20 Symbols for Circuit Elements Battery Resistor Capacitor Switch P12-21 Sign Conventions - Battery Moving from the negative to positive terminal of a battery increases your potential V Vb Va Think: Ski Lift P12-22 Sign Conventions - Resistor Moving across a resistor in the direction of current decreases your potential V Vb Va Think: Ski Slope P12-23 Sign Conventions - Capacitor Moving across a capacitor from the negatively to positively charged plate increases your potential V Vb Va Think: Ski Lodge P12-24 Series vs. Parallel Series Parallel P12-25 Resistors In Series The same current I must flow through both resistors V I R1 I R2 I ( R1 R2 ) I Req Req R1 R2 P12-26 Resistors In Parallel Voltage drop across the resistors must be the same V V1 V2 I1R1 I 2 R2 IReq V V V I I1 I 2 R1 R2 Req 1 1 1 Req R1 R2 P12-27 Measuring Voltage & Current P12-28 Measuring Potential Difference A voltmeter must be hooked in parallel across the element you want to measure the potential difference across Voltmeters have a very large resistance, so that they don’t affect the circuit too much P12- Measuring Current An ammeter must be hooked in series with the element you want to measure the current through Ammeters have a very low resistance, so that they don’t affect the circuit too much P12- Measuring Resistance An ohmmeter must be hooked in parallel across the element you want to measure the resistance of Here we are measuring R1 Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery) P12- Experiment 6: Simple Circuits P12-32 PRS Questions: Light Bulbs P12-33 Kirchhoff’s Loop Rules P12-34 Kirchhoff’s Rules 1. Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction. I1 I 2 I 3 P12-35 Kirchhoff’s Rules 2. Sum of potential differences across all elements around any closed circuit loop must be zero. V E d s 0 Closed Path P12-36 Internal Resistance Real batteries have an internal resistance, r, which is small but non-zero Terminal voltage: V Vb Va I r (Even if you short the leads you don’t get infinite current) P12- Steps of Solving Circuit Problem 1. 2. 3. 4. 5. Straighten out circuit (make squares) Simplify resistors in series/parallel Assign current loops (arbitrary) Write loop equations (1 per loop) Solve P12-38 Example: Simple Circuit You can simplify resistors in series (but don’t need to) What is current through the bottom battery? P12-39 Example: Simple Circuit Start at a in both loops Walk in direction of current 2 I1R I1 I 2 R 0 I 2 I1 R 0 Add these: 2 I1 R 0 I1 R We wanted I2: I 2 I1 R I 2 I2 0 R I1 P12-40 Group Problem: Circuit Find meters’ values. All resistors are R, batteries are HARDER EASIER P12-41