P WARNING: Exam is Thursday, 7:30 – 9 pm Room Review Sessions: Me: Tuesday 4-6 pm6-120 Imran:Wednesday8-10 pm4-270 In class:Thursday12-2 pm; 2-4 pm Office Hours: Brian F.:Tuesday8-10 pm6-402 Brian P.:Wednesday4-6 pm6-106 Please me questions

P Class 12: Outline Hour 1: DC Circuits Hour 2: Expt. 6: Simple Circuits

P Last Time: Capacitors & Dielectrics

P12 - Capacitors & Dielectrics To calculate: 1) Put on arbitrary ±Q 2) Calculate E 3) Calculate  V Dielectrics Energy Capacitance

P12 - This Time: DC Circuits

P Examples of Circuits

P Current: Flow Of Charge Units of Current: Coulombs/second = Ampere Average current I av : Charge  Q flowing across area A in time  t Instantaneous current: differential limit of I av

P Direction of The Current Direction of current is direction of flow of pos. charge or, opposite direction of flow of negative charge

P Current Density J J: current/unit area points in direction of current

P 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 E inside ≠ 0)!

P 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?

P Conductivity and Resistivity  : conductivity  : resistivity Ability of current to flow depends on density of charges & rate of scattering Two quantities summarize this:

P Microscopic Ohm’s Law  and  depend only on the microscopic properties of the material, not on its shape

P Demonstrations: Temperature Effects on 

P PRS Questions: Resistance?

P Why Does Current Flow? Instead of thinking of Electric Field, think of potential difference across the conductor

P Ohm’s Law What is relationship between  V and current?

P Ohm’s Law R has units of Ohms (  ) = Volts/Amp

P Examples of Circuits

P 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!

P Symbols for Circuit Elements Battery Resistor Capacitor Switch

P Sign Conventions - Battery Moving from the negative to positive terminal of a battery increases your potential Think: Ski Lift

P Sign Conventions - Resistor Moving across a resistor in the direction of current decreases your potential Think: Ski Slope

P Sign Conventions - Capacitor Moving across a capacitor from the negatively to positively charged plate increases your potential Think: Ski Lodge

P Series vs. Parallel Series Parallel

P Resistors In Series The same current I must flow through both resistors

P Resistors In Parallel Voltage drop across the resistors must be the same

P Measuring Voltage & Current

P12 - 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 R 1 Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery)

P Experiment 6: Simple Circuits

P PRS Questions: Light Bulbs

P Kirchhoff’s Loop Rules

P Kirchhoff’s Rules 1.Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction.

P Kirchhoff’s Rules 2. Sum of potential differences across all elements around any closed circuit loop must be zero.

P12 - Internal Resistance Real batteries have an internal resistance, r, which is small but non-zero Terminal voltage: (Even if you short the leads you don’t get infinite current)

P Steps of Solving Circuit Problem 1. Straighten out circuit (make squares) 2. Simplify resistors in series/parallel 3. Assign current loops (arbitrary) 4. Write loop equations (1 per loop) 5. Solve

P Example: Simple Circuit You can simplify resistors in series (but don’t need to) What is current through the bottom battery?

P Example: Simple Circuit Start at a in both loops Walk in direction of current Add these: We wanted I 2 :

P Group Problem: Circuit HARDEREASIER Find meters’ values. All resistors are R, batteries are 