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Putting this together: Electric Force Voltage and circuits opposite charges attract like charges repel F - - F - F F + Consider 2 ‘point’ charges, A and B. What force does charge A feel? qA How are these the same thing? Lecture 21 : Electrical potential energy Voltage Starting Circuits. + - --- -- + - + -- + - + + Wall at first Remember force between charges = 𝒌 + + + 𝒒𝑨 𝒒𝑩 𝒓𝟐 - 𝒒𝑨 𝒒𝑩 𝒓𝟐 Mechanical work vs. Electrical - Think, climbing up a hill stores energy in system - Same thing, separating charges… Polarized wall Electrons are repelled but can’t get too far • Electrons in balloon are then ATTRACTED to the positive charges • They are REPELLED from the negative ones. • The repulsion is smaller because r is bigger Discussion of Energy • 3 Types of energy (there are others): Kinetic - energy of motion - rock rolling down hill Potential - ability to do work in future - rock at the top of a hill or a fluid has it under pressure. Thermal - energy that dissipates as heat (e.g. friction, or smashing into a wall) • How would this apply to charges? + 𝑭𝒐𝒏 𝑩 𝒇𝒓𝒐𝒎 𝑨 = 𝒌 Reminders: HW 9 due thursday Reading for Tuesday:??? How does a charged particle attract a neutral one? --- qB • k is Coulomb constant = 9 x 109 N m2/C2 • qA and qB are amount of charge in coulombs (C ) • r is separation in m • negative sign means attraction Remember the balloon and the wall? --- r - • Think of the analogy of a hill… pulling + away from valley… - F F + We just have to be more careful because unlike mass (all masses attract each other) some charges attract while others repel Hill Analogy for energy Effort (push) to get ball (at constant speed): up the hill a) harder at first b) easier at first c) takes same effort / push The force required is related to the steepness or slope of the potential energy curve. Steeper means more force. 1 Voltage Hill Analogy for energy Potential Energy of same ball a a) PEa > PEb b b) PEb > PEa c) PEa = PEb http://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html Voltage has to do with conditions of system • Amount of charge • Distance from that charge • Like the electric force (related but different) Topo- practice • Which figure goes with #4 Voltage is like the height of mountain • Think Topographical maps Voltage tells you what a + charge will do +5V -5V +V is like top of hill -V Is like valley 0V • Answer C Where is 0 V? What will a +q do at 0V: a) Be attracted to higher voltage b) Be attracted to lower voltage c) Not be impacted b) Just like a ball rolls down hill 2 Voltage is like the height of mountain • Height (and gravity) • Voltage • Mass, m • Charge, q • Electrical Potential Energy • Gravitational potential Energy EPE = q D V GPE = m g Dh Electrostatic potential energy and voltage New force: Electrostatic force between charges New PE: Electric Potential Energy (EPE) Forces and PE go in pairs - Remember gravitational force: - Do work against gravitational force (mg) to raise an object’s GPE (mgh) - Similarly, do work against electric force to raise an object’s EPE EPE = q DV, where q = charge of object and DV is voltage difference Like GPE with q m and DV gDh Voltage (V) - tells you EPE of any charge at that location in space - Tells you work required to bring a unit charge from V = 0 to that location - Determined by surrounding charges. Closer you are to + charge the more + the voltage - A grounded object is always at V = 0. Grounded means attached to the ground! - Always interested in DV: voltage difference between 2 locations like GPE where only Dh mattered Best understood by doing practice questions! Two metal plates connected by a battery. Battery maintains a voltage difference of V between the plates Conservation of energy and EPE Remember conservation of energy equation: A - Work Done on object = Change in Energy of object Wext - Wfriction = DPE + DKE - Now we can add another PE term to this equation: q ++ - V + + + + + + B V Plate A-is grounded (set to zero V) What is the voltage of plate B? Wext - Wfriction = DGPE + DEPE + DKE = mgDh + qDV + D(1/2mv2) A q + + + + + + ++ a) b) c) d) B 0 +V -V - determine from information given Can’t q A ++ - - V + + + + + + B EPE = qDV - What will happen to the charge q if we let go of it (ignore gravity)? What is the change in EPE of charge as it flies from plate B to plate A? a) Nothing b) It will fly over to plate A c) Sparks will fly d) -Something else a) b) c) d) 0 +qV -qV Can’t determine - 3 CT 29.4b q A - + + + + + + ++ - V B Conservation of energy: Wext - Wfriction= DGPE + DEPE + DKE Did the electric potential energy (PE) increase or decrease? Did the voltage (V) at the position of the test charge increase or decrease? A: PE , V C: PE , V E: None of these. Charged particle loses EPE as it flies from B to A. What form has this energy turned into just before it hits plate A a) b) c) d) A positive charge q is released from position i to position f between the charged plates. - B: PE , V D: PE , V KE Thermal energy GPEPPE ©University of Colorado, Boulder (2008) CT 29.4 A negative charge -q is released from position i to position f between the charged plates of a charged capacitor. Electrostatics Summary Did the potential energy (PE) increase or decrease? Did the voltage (V) at the position of the test charge increase or decrease? • Positive and negative charge: Like charges repel, opposites attract • Coulombs law for point charges: F = k qA qB r2 Force acts along line joining particles A: PE , V B: PE , V C: PE , V D: PE , V E: None of these. • Voltage: Determines EPE of charge at that location in space Close to + charges voltage is more + and vice versa Grounded object is at 0V Hint: EPE = qDV (Also called Electric Potential) • EPE: = qDV New form of potential energy Lots of analogies to GPE (DVDh, qm) ©University of Colorado, Boulder (2008) Flashlights, circuits, batteries, and power light bulb circuit + + = • Given batteries, light bulbs, and wire, how can we design a light bulb circuit a) that will burn brightest, b) that will last longer, c) that will be dim, d) that will turn on and off. • How can you control and predict current and power in light bulbs? • All this basic circuit stuff applies to home wiring, home electronics, heaters etc. • Thursday lecture … help save lives … physics of dangers of electrocution. Builds on electrostatics (like charges repel, opposite charges attract, voltage, EPE) ………but now electrons are moving………………… ………. need to start thinking like an electron! • Start by looking at a really simple circuit containing - light bulb - Battery - Wires • Each element made of metal containing electrons that are free to move • What are the electrons doing in each element to ensure that the light bulb lights up? + Using each of these three elements can you draw a picture where the bulb lights up? 4 light bulb circuit: Wiring See this in action! What will happen when hook up positive end of battery (+) to flashlight bulb with one wire? a. light up b. barely light up c. not light up - + http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc Circuits so far a. b. c. d. e. Wires: Make complete circuit necessary for steady flow of electrons Usually have negligible (zero) resistance Battery: Maintains a voltage difference DV between terminals Provides each electron with qDV = eV of EPE to spend in circuit Provides push for electrons around circuit (bigger V, bigger push) Bulb: Filament is a high resistance wire KE of electrons converted into heat via collisions Electron rules for analyzing circuits a) No electron deaths/births b) No passing of electrons c) Electrons have energy (high at start, low at end) d) Different conducting materials have different resistances Think like an electron! a. b. c. d. e. Light will not light up, No current will flow Light will light up, Current will flow Light will barely light up, Current will flow Light will not light up, Current will flow Light will light up, No current will flow. Light will not light up, No current will flow Light will light up, Current will flow Light will barely light up, Current will flow Light will not light up, Current will flow Light will light up, No current will flow. back to signal and battery applets for review as needed Circuit language Resistance (R) of a circuit element is measure of how hard it is for electrons to pass through. Units: Ohms (W) What if increase voltage difference across battery? a. Rate at which electrons pass through filament stays the same b. Rate at which electrons pass through filament decreases c. Rate at which electrons pass through filament increases Current (I) : charge per second flowing past a point in the circuit (= # electrons per second × charge on electron) Units : Amps (1 A = 1 C/s) Voltage (difference) (DV) Vbatt a) Across battery: Measure of EPE given to each e- as it passes through battery. EPE given = eV. Related to pushing force on electrons in circuit b) Across a resistor (wire, filament etc): Measure of EPE lost by each e- as it passes through. EPE lost = eV. Unless told otherwise voltage difference across connecting wire = 0. Units: Volts (V) Note: All quantities specific to one component. Ohm’s Law: DV = IR Resistance of component Current through component Don’t mix and match! Voltage dropped across component 5 Electrical Power 1.5A If the battery on the left has a voltage (difference) of 6V and it is pushing a current of 1.5 A through the bulb, what is the resistance of 9W thea) bulb? b) 6 W c) 4 W d) 1.5 W e) 0 W What is the electrical power used up by each component in circuit? POWER tells us how HOT something gets or how BRIGHT a bulb is P = I DV Don’t mix and match! Voltage dropped across component Current through component Electrical power dissipated (used up) in component Also Ohm’s Law: D V = IR Substitute into power law to get different forms: P = DV2/R - I = V/R - Useful if you know V and R but not I (parallel circuits) 6V P = I2 R - V = IR - Useful if you know I and R but not V (series circuits) P = I DV - Useful if you know I and V but not R Power question I have a 60W bulb plugged into the mains. Assume that the mains supply is like a 120V battery What current flows through the bulb? a) 120A b) 60A c) 0.5A d) 2A e) 7200A Power question 60W I have a 60W bulb plugged into the mains. Assume that the mains supply is like a 120V battery 60W What current flows through the bulb? 0.5A 120V Batteries in series Batteries provide a voltage difference between their terminals If each battery below is an identical 3V battery, what is the total voltage across the following arrangement? a) 3V b) 0V c) 9V d) 6V e) Other V ? What is the resistance of the bulb filament? a) 240 W b) 2 W c) 0.5 W d) 30 W e) Can’t determine R 120V Batteries in series (nose to tail) case 1 Compare the brightness of the bulbs in case 1 and case 2. All bulbs and batteries are identical a. b. c. d. V 2 twice as bright as 1 2 same brightness but runs twice as long 2 much more than twice as bright as 1 2 produces no light R case 2 V V 6 R Batteries in parallel case 1 a. b. c. d. V R R Batteries in parallel Compare the brightness of the bulbs in case 1 and case 2. All bulbs and batteries are identical 2 twice as bright as 1 2 same brightness 2 much more than twice as bright as 1 2 produces no light What is the difference then? case 1 Each battery can produce a given amount of Current (electrons/ second) for a certain amount of time V R case 2 case 2 V V V V Note: rating on batteries is in AmpHours! (what is an amp-hour?) Zoinks.. All of a sudden, with two batteries I have a greater reservoir of electrons to draw from. Case 2: last twice as a long! R V V Summary: - Series: more energy for each electron! (brighter) how you make a 9 V out of D-Cells, or AAAs R - Parallel: longer lasting difference between AAAs and D cells Car battery demo 1 Ohms Law (V=IR) and Power (P = I DV) Connect paper clip across terminals. What will happen? a) nothing, b) drain battery slightly, c) melt paper clip, d) melt wires, e) both c. and d. c)Melt paper clip. How to figure out, how to explain? When analyzing circuits – think like an electron! V V Reasoning a little more mathematically e e + 12 V e - --------------- Melt paper clip. How to figure out? What current flows? • Paperclip and wires are in series Same current through each R = Rpaperclip+Rwires (very small) • I = DV/R R small I very big Power from battery? P = I DV Where does this power go? I large P large 2 - Power used in wire = I Rwire 2 - Power used in paperclip = I Rclip Power used depends only on resistance of component - Rpaperclip >> Rwire. - More electrical power heat in clip, so it melts. Wire not even hot. This is how (old) fuses worked. Car battery demo 2 Student volunteer grabs terminals with hands. A. Nothing. B. Will get zapped (flames etc.) like paperclip C. will get mild jolt, D. other How to figure out? 1st step in process? 1. How much electrical power goes into person? → If a lot, zapped and flames, but if tiny, volunteer will not notice. 2. What determines amount of power through person? P=DIV Voltage (DV) set by battery =12V. Current (I) = DV/R. Rperson is high, so for 12 V, I is very small. P is very small. 3. That’s the theory… how do we test? Experiment…….. 7 Avoiding electrocution- ohms law applied to the human body. Avoiding electrocution- ohms law applied to the human body. Extent of injuries are determined by 2 factors: Extent of injuries are determined by 2 factors: a) The amount of current that flows b) Where it flows through the body a) The amount of current that flows b) Where it flows through the body Rules of thumb: • 1-5 mA you can barely feel • 10 mA is painful • 100 mA causes muscle contraction in the heart, can be lethal Rules of thumb: • 1-5 mA you can barely feel • 10 mA is painful • 100 mA causes muscle contraction in the heart, can be lethal Resistance of dry skin ~105 ohms Resistance of wet skin ~ 1000 ohms (but with wide variations) Resistance of dry skin ~105 ohms Resistance of wet skin ~ 1000 ohms (but with wide variations) So: if 10,000 volts is applied briefly across a person’s dry chest, what happens? a. no effect b. sure electrocution without immediate treatment c. painful but recover immediately d. vaporize person Don’t try this at home Applying 120 volts between right arm and right foot a. no effect b. fibrillation and electrocution c. painful but probably no significant damage So: if 100 volts is applied briefly across a person’s dry chest, what happens? a. no effect b. sure electrocution without immediate treatment c. painful but recover immediately d. vaporize person Don’t try this at home 120 V Applying 120 volts to wet left hand, right hand in pocket and wearing rubber sole shoes a. little effect b. fibrillation and electrocution c. painful but probably no significant damage Don’t try this at home 120 V Applying 120V between wet left hand and wet feet a. little effect b. fibrillation and electrocution c. painful but probably no significant damage 8