Charging by Conduction (in conductors) Like charges repel each other Electrons want to travel to the ground or to some place less crowded so they can spread out Before After © RHJansen

Charging by Friction Rubbing two substances together can transfer outer electrons from one material to the other. (Example balloon and wool) Electrons are pulled from the wool to the balloon. – + – The balloon has more electrons than usual. The balloon: – charged, The wool: + charged wool

Remember when Charging by Friction … Rubbing materials does NOT create electric charges. It just transfers electrons from one material to the other.

Polarization Separation of charges in a neutral object. Net charge of object remains zero!

Equipotential Lines Electric Fields & (VOLTAGES) Point Charge Di-Pole

Electric Fields & Equipotential Lines Two Neg Point Charges Equipotentials & E-field Arrows Equipotential Lines

Electric Fields & Equipotential Lines Lines of Charge: Charged Parallel Conducting Plates

Capacitors Charged Parallel Conducting Plates

WHAt capacitors really look like Some typical capacitors. Size and value of capacitance are not necessarily related. (credit: Windell Oskay)

Dielectric is Insulator Capacitors Dielectric is Insulator Placed Between Conducting Plates. Charged Capacitor POLARIZES the Dielectric

Conductors, Charge, & Electric Fields Charges are free to move on conductors The E-Field from on charge pushes the other charges away Charges on a Conductor are pushed to the outside of the conductor On a charged conductor, the E-field lines are perpendicular to the conductor surface

Conductors in External Electric Fields Electric fields polarize charges. The charges move to counteract the field that’s acting on them. This cancels the effect of the E-field inside the neutral conductor

Conductors and Electric Fields The electric field inside a conductor is always zero for electrostatic equilibrium. The electric field outside a conductor is always perpendicular to the surface It is stronger for sharper points, and weaker for flatter surfaces.

Current, Resistance, & Voltage Video https://www.youtube.com/watch?v=1xPjES-sHwg

Current (Ch. 21.1) Charges Moving (Dynamic NOT Static) Current = Rate at which Charges Flow Symbol: I Units: Amp (A) –short for Ampere

How Do We Get Charges to Move? Connect a Charged Capacitor with a conducting wire This will create a conducting path form high to low electrical potential. A current (moving electric charges) will flow through the wire.

How Do We Get Charges to Move? The Electric Field in the Wire Applies a Force that Pushes Charges in the Wire from the + side to the – side.

Current Direction: Current Flows in SAME direction as Electric Field in the Conductor: + to  electrons flow from  terminal to + terminal

Practice Problem 1: (Ex. 20.2) If a 0.300 mA current through a calculator is carried by electrons, how many electrons per second pass through the calculator? Givens: I = 0.3x10-3 A Equation: Conversions: 1e- = 1.6x10-19 C Use Logic to Put it Together: =1.881015 e-/s

Current Flow Exercise: Everyone, please stand and form a loop Cotton Balls are Electrons Due to Coulomb Repulsion, CAN NOT HAVE TWO COTTON BALLS IN HAND AT SAME TIME!!! Only pick up neighboring ball IF your other hand is Empty.

Current Flow Exercise: Drift Velocity: Current Flow Exercise: Current Moves almost Instantaneously when Voltage (Electric Potential) is applied to a conductor Individual electrons move MUCH SLOWER in the conductor How fast did the cotton balls move? How long did it take to STOP the cotton balls moving?  +++

How can we detect current? connecting wire gets warm A lightbulb glows. The bulb filament is part of connecting wire. A compass needle gets deflected (electromagnetism)

Ohm’s Law: Resistance & Simple Circuits Resistance Symbol: R Unit = Ohms,  - the abbreviation symbol for Ohms Definition Resistance: determines how easily current can flow through a material

On a CONDUCTOR, electrons are free to move Electrons on an INSULATOR do NOT move easily

Resistance in a circuit is a natural thing. ALL conductors have some resistance. Good conductors, like copper, have a small resistance values. Insulators have VERY high resistance values. Electrical Resistance is like rocks in the stream, the slow down the current flow.

Resistance Resistance in a Wire is like trying to walk down a crowded hallway How do you increase current? More people move in your direction (increase Voltage) Reduce # of people in hallway (better conductor) Increase the width of the hallway ( diameter wire) Shorten hallway – get to other side faster (shorter wire) Reduce temperature (harder to move past people or molecules with a lot of internal kinetic energy)

Resistivity,  (units: /m) (Ch. 21.3) Resistance in a wire depends on: length of wire cross-sectional area of wire resistivity of material (Table 20.1)

In electric circuits it is important to control the flow of current To do this we use little resistors that can effect the flow of electrons. Picture of Resistors Symbols for Resistors

Circuit Drawing with Resistors

OHM’S LAW V = IR V I R

OHM’S LAW FORMULAS V = I R Find Current Find Voltage Find Resistance I = V R R = V I V = I R Current equals voltage divided by resistance Voltage equals current multiplied by resistance Resistance equals voltage divided by current

Practice Problem (example 20 Practice Problem (example 20.4) What is the resistance in an automobile headlight through which 2.50 Amps flows when 12 Volts is applied? Givens: I = 2.5 A V = 12V R = ? Equation: Conversions: Use Logic to Put it Together: =4.80 

White Boards: Solve using Ohm’s Law: V=IR ANS: I = 0.36 A ANS: V = 120 V ANS: R = 1.5x104 

Whiteboards Solve using Ohm’s Law: V=IR 1. 2. 3. V = IR so I = V/R I = (12 V)/(33) = 0.364 A I = 0.36 A R=33 V = 12 V V = IR V = (3.8 A)(32) = 121.6 V V = 120 V R=32 I = 3.8 A V = IR so R = V/I R = (3.0 V)/(2.0x10-4 A) = 15,000  R=1.5 x104  or R = 15 k I = 2.0x10-4 A V = 3.0 V

Ohm’s Law Does Not Always Apply Δ𝑉=𝐼𝑅 Ohmic devices Devices that obey Ohm’s law Non-ohmic devices Capacitors Diodes Batteries

Quick QUIZ: In which circuits will the bulbs light up Quick QUIZ: In which circuits will the bulbs light up? There must be a complete unbroken path so electrons can flow for bulbs to light! A B C

Quick QUIZ: In which circuits will the bulbs light up Quick QUIZ: In which circuits will the bulbs light up? There must be a complete unbroken path so electrons can flow for bulbs to light! A B C

Series Resistors What are resistors in series? Connected one after the other There is only one path One path means there can be only ONE CURRENT Each resistors has same current (I) If one breaks, all stop working

Current for SERIES Resistors is the SAME! Series Resistors – the current through each resistor is the same. The voltage across each resistor can be different! I I I I

A new idea: Equivalent Resistance (Req) Equivalent Resistance – you can replace any number of resistors with one equivalent resistor called Req

Equivalent Resistance (Req) for Series Resistors Just add them up!

Practice Problem: Series Resistors 25 Ω 150 Ω 125 Ω 30 V What is the equivalent resistance for the circuit? How much current goes through the 25 Ω resistor? How much current goes through the 150 Ω resistor?

Practice Problem: Series Resistors 25 Ω 150 Ω 125 Ω 30 V What is the equivalent resistance for the circuit? How much current goes through the 25 Ω resistor? How much current goes through the 150 Ω resistor? Req = 25+150+125 = 300  I =V/Req = 30V/300  = 0.1 A ONLY 1 CURRENT so I = 0.1 A

Voltage Drops in a Series Circuit Vbatt Vbatt V1 R1 Vbatt- V1 Vbatt R2 V2 Vbatt- V1-V2 = 0 V 0 V The electric potential drops as energy is used/dissipated by each resistor

Voltage Drop across Series Resistors 25 Ω 150 Ω 125 Ω 30 V Use Ohm’s Law to find V across each resistor Vn = IRn where n is the number identifying each resistor

Practice Problems: 25 Ω 150 Ω 125 Ω 30 V 0.1 A current flows through the circuit shown. Find the voltage drop across each resistor. What is the total voltage drop for this circuit? V1 = IR1=(0.1A)(25) = 2.5V V2 = IR2=(0.1A)(150) = 15V V3 =(0.1A)(125) = 12.5V Vtot = V1 + V2 + V3 =Vbatt = 2.5V + 15V + 12.5V = 30V

Parallel Resistors What are resistors in parallel? Each Resistor is Connected to the Battery There is more than one path Each Path has DIFFERENT CURRENT (I) Each resistors feels the same voltage (V) If one breaks, the rest keep working!

The total current is equal to the sum of the currents Parallel Resistors – the voltage difference across each resistor is the same Vtotal = V1 = V2 = V3 The total current is equal to the sum of the currents Itotal = I1+I2+I3 Itotal I1 I2 I3 V R1 R2 R3

Work in your notes: Example problem: Find Itot and Req 2) Find P across each Resistor Step 1: find I for each resistor I1 = V/R1 = (10V)/(2) = 5 A I2 = V/R2 = (10V)/(5) = 2 A I3 = V/R3 = (10V)/(10) = 1 A Step 2: Add the currents to get the Itot in the circuit Itot = I1 + I2 + I3 = 5A + 2A + 1A = 8 A

Example problem: Find Itot and Req 2) Find P across each Resistor Step 3: Find Req Req = Vbatt/Itot = (10V)/(8A) = 1.25  Step 4: Use P=V2/R to find Power used by each resistor P1 =(10V)2/(2) = 50 Watt P2 =(10V)2/(5) = 20 Watt P3 =(10V)2/(10) = 10 Watt Step 5: Ptot = P1 + P2 + P3 = 80 W or Ptot = (Itot)(Vbatt) = (8A)(10V) = 80 W

Parallel Circuits In a parallel circuit, there is more than one current path. To find the equivalent resistance: