Warm-up Suppose you want to connect your stereo to remote speakers. If each wire must be 20m long, what diameter copper wire (ρ = 1.68x10-8 Ωm) should you use to keep the resistance less than .10Ω per wire? Take out your skills homework to hand in. 1/31/08

Objectives Describe origination of charge flow in a circuit. Draw and interpret schematic diagrams. Explain operation of a capacitor. Discuss voltage and apply to series and parallel circuits. Describe charge flow during transient and steady-state processes. 1/31/08

Agenda Finish Resistance Castle Kits- Sections 2 and 3 Parallel and Series Discussion 1/31/08

Resistance of Wires For wires with a circular cross section, A = pr2 R = rL/A -------------------------------- The longer the wire, the larger its resistance. The larger the area, the smaller the resistance. R = rL/A    = rL/pr2 --------------------------------- The thicker the wire, the less its resistance 1/31/08

A = ρ (L/R) = (1.68 x 10-8 Ω m)(20 m)/ (0.10 Ω) Example You want to keep the resistance in your 20 m cooper (pg. 535) speaker wires to less than 0.10 Ω per wire. What diameter wire should you use? A = ρ (L/R) = (1.68 x 10-8 Ω m)(20 m)/ (0.10 Ω) = 3.4 x 10-6 m2 Cross sectional area is related to diameter by A = pd2/4 Therefore d = 2.1 mm 1/31/08

CASTLE Kit Section 2 Light bulbs are resistors; both allow charge to flow but at a lower rate than a conductor Flow rate is NOT the same as speed Wires have resistance 1/31/08

Symbology Pg. 530, 532, 534, 513 Batteries Wires Resistors/bulbs Capacitors 1/31/08

Conventional Current Conventional current flows in the direction a positive charge would move, even though this is opposite the flow of electrons 1/31/08

Charge Conventional meaning of + and – True meaning of + and – + is a more than normal charge - is a less than normal charge True meaning of + and – + is an absence of charge - is an excess of charge 1/31/08

Circuit Diagrams Draw diagram of circuit with 3 batteries and 2 bulbs. Use arrow(s) to indicate the direction of conventional charge flow. 1/31/08

Flow of Charge Charge flows when there is a potential difference (or difference in voltage) between the ends of a conductor When there is no potential difference, there is no current flow The ampere is the unit of current flow An ampere is a current flow of one coulomb of charge per second (6.24 billion billion electrons) 1/31/08

Current is Flow of Charge A steady current of 2.5 A flows in a wire for 4.0 min. How much charge passed through any point in the circuit? How many electrons was that? 2.5 A = 2.5 C/s (4.0 minutes = 240 s) ∆Q = I ∆t = (2.5 C/s) (240 s) = 600 C To count electrons (600 C) / (1.6 x 10-19 C/electron) = 3.8 x 1023 electrons 1/31/08

Current Flow and Resistance The current flowing in a circuit depends on the Voltage (sort of like the pressure in a hose) Resistance to the flow of current (the diameter of the hose) All elements in a circuit resist the flow of current to some degree Things that use electricity to do work (lights, motors, etc.) have relatively high resistance These are called electrical loads Other parts of the circuit (wires, switches, etc.) have relatively low resistance. 1/31/08

Parallel Resistors Parallel pair has less resistance than a single bulb. Lower resistance lets same pressure differences drive more flow. Circuit has lower resistance but equal pressure differences (total) as earlier circuit. 1/31/08

Ohm’s Law voltage resistance current = or I = V/R and V = I R The unit of resistance is the ohm and its symbol is Ω 1/31/08

Ohm’s Law Example A nine volt battery supplies power to a cordless curling iron with a resistance of 18 ohms. How much current is flowing through the curling iron? 1/31/08

Ohm’s Law Examples 1/31/08

CASTLE Kit Section 3 Charge originates in all parts of circuit at once. Capacitors Batteries have internal resistance. 1/31/08

Where does charge originate? Activity 3.5: Set up circuit using ROUND BULBS and BLUE CAPACITOR What happens to the compass during the charging of the capacitor? Discharging? Draw schematic that shows flow. 1/31/08

Capacitor 2 layers of conducting material separated by insulator Capacitor plates Terminals Capacitance Farad 1/31/08

Series Capacitor Charge The charge on capacitors in series is the same. 1/31/08

Capacitors in Series Example: C1 = 30  μF C2 = 60  μF 1/Cs = 1 / 30 + 1/60         = 3 / 60         = 1 / 20    Cs = 20  μF  1 / Cs = 1 / C1 + 1 / C2 1/31/08

Voltage on Capacitors in Series CA = 50 x 10-6 F     CB = 10 x 10-6 F VA = Q / CA        = 2 V  VB = Q / CB        = 10 V Q is the same on each capacitor.   By Kirchhoff's Loop Rule: 12 - Q / CB - Q / CA = 0   Q =  1 x 10-4 C 1/31/08

Capacitors in Parallel Example: C1 = 30  μF C2 = 60  μF  Cp = 30 + 60        = 90  μF  Cp = C1 + C2 1/31/08

Charge on Capacitors in Parallel Each capacitor sees same voltage:   100 V C = Q/V (basic definition) Q = CV Q1 = (5)(100)      = 500 C Q2 = (2)(100)      = 200 C 1/31/08

Are batteries necessary? Activity 3.7: Use the genecon to light 2 bulbs in a circuit. Where does the charge originate with a genecon? 1/31/08

Energy conversion In which case is more energy converted? Discharging a capacitor through long bulbs? Discharging a capacitor through round bulbs? What are the energy conversions? 1/31/08

Why does charging of a capacitor stop? Charge blue capacitor thru 2 long bulbs with 3 cell battery. Use compass to monitor flow. Add another 3 cell battery. Monitor flow. Discharge the capacitor through the bulbs. 1/31/08

Closure Check Your Understanding: Homework: Explain how a capacitor charges and why it stops taking charge. Homework: Week 1 homework due Monday (should definitely be “half-way” by now “Ready” for Ohm’s Law Lab by Tuesday Quiz Tuesday 1/31/08