* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapters 18 and 19
Survey
Document related concepts
Valve RF amplifier wikipedia , lookup
Schmitt trigger wikipedia , lookup
Galvanometer wikipedia , lookup
Superconductivity wikipedia , lookup
Electric battery wikipedia , lookup
Operational amplifier wikipedia , lookup
Power electronics wikipedia , lookup
Rechargeable battery wikipedia , lookup
Power MOSFET wikipedia , lookup
Electrical ballast wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Surge protector wikipedia , lookup
Opto-isolator wikipedia , lookup
Current source wikipedia , lookup
Current mirror wikipedia , lookup
Transcript
Chapter 18 Electric Currents 18.1 The Electric Battery First battery – consisted of two dissimilar metals connected by a conductive solution called an electrolyte. The Electric Battery • A battery transforms chemical energy into electrical energy. • Chemical reactions within the cell (or solar energy) create a potential difference between the terminals • Called the “Electro Motive Force” or EMF (ε) • Not really a force, unit is the volt Moving Charges = current Conductor + + + + Chuck E Cheese wrist watch Current = (amount of charge going by)/(time) 18.2 Electric Current Electric current is the rate of flow of charge through a conductor: (18-1) Unit of electric current: the ampere (Amp), A. 1 A = 1 C/s. Electric Circuit Components + ε Battery - Capacitor C R Resistor 18.2 Electric Current In order for current to flow, there must be a path from one battery terminal, through the circuit, and back to the other battery terminal. Only one of these circuits will work: 18.2 Electric Current By convention, current is defined as flowing from + to -. Electrons actually flow in the opposite direction, but not all currents consist of electrons. 18.3 Ohm’s Law: Resistance and Resistors Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends: 18.3 Ohm’s Law: Resistance and Resistors The ratio of voltage to current is called the resistance: (18-2a) (18-2b) 18.3 Ohm’s Law: Resistance and Resistors In many conductors, the resistance is independent of the voltage; this relationship is called Ohm’s law. Materials that do not follow Ohm’s law are called nonohmic. Unit of resistance: the ohm, Ω. 1 Ω = 1 V/A. Some clarifications: • Batteries maintain a (nearly) constant potential difference; the current varies. • Resistance is a property of a material or device. • Current is not a vector but it does have a direction. • Current and charge do not get used up. Whatever charge goes in one end of a circuit comes out the other end. 18.4 Resistivity The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area: The constant ρ, the resistivity, is characteristic of the material. 18.4 Resistivity 18.4 Resistivity For any given material, the resistivity changes with temperature: Since R T R 0 1 T - T0 R0 = Resistance at some reference temperature (T0) α = temperature coefficient and R = resistance at some new temperature T If positive, if T , R If negative if T , R Semiconductors are complex materials, and may have resistivities that decrease with temperature. 18.4 Resistivity 18.8 Microscopic View of Electric Current When a potential difference is applied across a conductor, the electrons acquire an average drift velocity (vd) as they move through the medium, colliding with imperfections, atomic motions, etc.. Volume = LxA and L = vd x Δt Length = L Area = A 18.8 Microscopic View of Electric Current This drift speed is related to the current in the wire, and also to the number of electrons per unit volume (n) which depends on the material. Q (within region) Number of Charges x Charge of each one Q n(Volume)( e) nAv d t(e) I j nev d A Length = L Area = A V (voltage) E = V/L Macroscopic Quantities R Microscopic Quantities ρ Relationship V E V=EL I j = n e vd I=jA L R ρ A 18.5 Electric Power Power, as in kinematics, is the energy transformed by a device per unit time: 18.5 Electric Power The unit of power is the watt, W. 1Watt = 1 Joule/second Power • • • • • Power = Energy/time Unit = 1 watt = 1J/s You are billed for electrical energy use E = (P)(t) = kw-hr 100 W light bulb for one day E (100 watts)(24 hrs)(3600 s/hr) 8.6 10 J 2000 kcal 6 Heat • Unit = kcal (heat required to raise 1 kg of water 10 C) • 1 kcal = 4.18 x 103 J (Food Calorie) 18.7 Alternating Current Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC). 18.7 Alternating Current The voltage varies sinusoidally with time: as does the current: (18-7) 18.7 Alternating Current Multiplying the current and the voltage gives the power: 18.7 Alternating Current Usually we are interested in the average power: 18.7 Alternating Current The current and voltage both have average values of zero, so we square them, take the average, then take the square root, yielding the root mean square (rms) value. (18-8a) (18-8b) 18.9 Superconductivity In general, resistivity decreases as temperature decreases. Some materials, however, have resistivity that falls abruptly to zero at a very low temperature, called the critical temperature, TC. 18.9 Superconductivity Experiments have shown that currents, once started, can flow through these materials for years without decreasing even without a potential difference. Critical temperatures are low; for many years no material was found to be superconducting above 23 K. More recently, novel materials have been found to be superconducting below 90 K, and work on higher temperature superconductors is continuing. Summary of Chapter 18 • Ohmic materials have constant resistance, independent of voltage. • Resistance is determined by shape and material: • ρ is the resistivity. Summary of Chapter 18 • Power in an electric circuit: • Direct current is constant • Alternating current varies sinusoidally Summary of Chapter 18 • The average (rms) current and voltage: • Relation between drift speed and current: Chapter 19 DC Circuits Conservation Laws • Conservation of Charge (I = Q/t) and I • Conservation of Energy (PE = QV) and V • Conservative Forces (pages 148-149) • ∑ of Work around a closed path = 0 • Independent of Path • For a closed loop ∑ of PE gained and lost or ∑ of V gained and lost = 0 Conservation Laws I ε + - R Conservation of Charge (I = Q/t) and I I out of battery = I into resistor = I out of resistor = I into battery Conservation of Energy (PE = QV) and V Analogy Baseballs Heavy oil Person does work to lift baseballs, they gain energy Baseballs fall through heavy oil and loose energy Oil heats up. Energy in = energy out I ε + VH - VL VA R VB Battery does work and energy increases by Qε Where ε = (VH - VL) As charge goes through resistor energy is lost (QV) where V = VA - VB Qε - QV = 0 ε=V I ε + - ε-V = 0 ε –IR =0 ε = IR Simple Circuit R V = IR Simple Circuits I R1 ε + R2 ε – IR1 – IR2 = 0 ε – I(R1 + R2)= 0 ε= V1 + V2 EMF and Terminal Voltage This resistance behaves as though it were in series with the emf. a and b are the terminals of the battery I Going around circuit ε – Ir – IR = 0 a r ε R + b Va - Vb = ε - Ir EMF and Terminal Voltage Electric circuit needs battery or generator to produce current – these are called sources of emf. Battery is a nearly constant voltage source, but does have a small internal resistance, which reduces the actual voltage from the ideal emf: (19-1) Resistors in Series A series connection has a single path from the battery, through each circuit element in turn, then back to the battery. Resistors in Series The current through each resistor is the same; the voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage. (19-2) V = V1 + V2 + V3 V = IR1 + IR2 + IR3= IReq Resistors in Series From this we get the equivalent resistance (that single resistance that gives the same current in the circuit). Resistors in Parallel A parallel connection splits the current; the voltage across each resistor is the same: ∑ V around closed path = 0 Independent of Path V = I1R1 V = I2R2 V = I3R3 Resistors in Parallel The total current is the sum of the currents across each resistor: Resistors in Parallel This gives the reciprocal of the equivalent resistance: (19-4) Repeat this Mantra • The current is the same for elements connected in series • The voltage is the same for elements connected in parallel Light Bulbs Rated by Power across 120 volts Examples: 50 watts @ 120 volts; 100 watts @ 120 volts Which has higher resistance? 2 2 V V P IV I R ; R R P 2 120 volts For 50 W bulb R 2 288 50 W 2 120 volts For 100 W bulb R 144 100 W Resistors in Series and in Parallel What is Equivalent Resistance? 1 1 1 3 6Ω 3Ω R EQ 6Ω R EQ 2Ω R EQ 4Ω 2Ω 6Ω Resistors in Series and in Parallel What is Current through the 6Ω Resistor? From (c) I = 3A and V across 6Ω resistor = 18V I through 4Ω and 2Ω resistors = 3A V across 6Ω and 3Ω resistors = 6V 19.3 Kirchhoff’s Rules Some circuits cannot be broken down into series and parallel connections. Multiple Loop Game Rules • Draw picture • Define number of loops • Pick ARBITRARY directions for the currents • Indentify branch points (where currents divide) • Currents into branch points = currents out of branch points • Circle each loop and ∑ V’s = 0 How to circle a loop • Start at some ARBITRARY point • Circle clockwise or counterclockwise (your choice) • End at starting point How to Add V’s When you come to a Battery as you circle the loop ε -ε Direction you take +ε When you come to a Resistor as you circle the loop you will travel with or against the current R I - IR + IR 19.4 EMFs in Series and in Parallel; Charging a Battery EMFs in series in the same direction: total voltage is the sum of the separate voltages 19.4 EMFs in Series and in Parallel; Charging a Battery EMFs in series, opposite direction: total voltage is the difference, but the lowervoltage battery is charged. 19.4 EMFs in Series and in Parallel; Charging a Battery EMFs in parallel only make sense if the voltages are the same; this arrangement can produce more current than a single emf. 19.5 Circuits Containing Capacitors in Series and in Parallel Capacitors in parallel have the same voltage across each one: 19.5 Circuits Containing Capacitors in Series and in Parallel In this case, the total capacitance is the sum: (19-5) 19.5 Circuits Containing Capacitors in Series and in Parallel Capacitors in series have the same charge: 19.5 Circuits Containing Capacitors in Series and in Parallel In this case, the reciprocals of the capacitances add to give the reciprocal of the equivalent capacitance: (19-6) 19.6 RC Circuits – Resistor and Capacitor in Series When the switch is closed, the capacitor will begin to charge. 19.6 RC Circuits – Resistor and Capacitor in Series The voltage across the capacitor increases with time: This is a type of exponential. 19.6 RC Circuits – Resistor and Capacitor in Series The charge follows a similar curve: This curve has a characteristic time constant: (19-7) 19.6 RC Circuits – Resistor and Capacitor in Series If an isolated charged capacitor is connected across a resistor, it discharges: 19.7 Electric Hazards Even very small currents – 10 to 100 mA can be dangerous, disrupting the nervous system. Larger currents may also cause burns. Household voltage can be lethal if you are wet and in good contact with the ground. Be careful! 18.6 Power in Household Circuits The wires used in homes to carry electricity have very low resistance. However, if the current is high enough, the power will increase and the wires can become hot enough to start a fire. To avoid this, we use fuses or circuit breakers, which disconnect when the current goes above a predetermined value. 18.6 Power in Household Circuits Fuses are one-use items – if they blow, the fuse is destroyed and must be replaced. 18.6 Power in Household Circuits Circuit breakers, which are now much more common in homes than they once were, are switches that will open if the current is too high; they can then be reset. 19.7 Electric Hazards The safest plugs are those with three prongs; they have a separate ground line. Here is an example of household wiring – colors can vary, though! Be sure you know which is the hot wire before you do anything. 19.7 Electric Hazards A person receiving a shock has become part of a complete circuit. 2 prongs vs. 3 prongs 19.7 Electric Hazards Faulty wiring and improper grounding can be hazardous. Make sure electrical work is done by a professional. 19.8 Ammeters and Voltmeters An ammeter measures current; a voltmeter measures voltage. Both are based on galvanometers, unless they are digital. The current in a circuit passes through the ammeter; the ammeter should have low resistance so as not to affect the current. 19.8 Ammeters and Voltmeters A voltmeter should not affect the voltage across the circuit element it is measuring; therefore its resistance should be very large. 19.8 Ammeters and Voltmeters An ohmmeter measures resistance; it requires a battery to provide a current I want to measure Current and Voltages in this Circuit without disturbing the Circuit I use Ammeters and Voltmeters Ammeters – Very small resistance so voltage across it is very small In series Voltmeters - Very large resistance, takes away little current. In Parallel What would happen if I put an Ammeter in Parallel? A Summary of Chapter 19 • A source of emf transforms energy from some other form to electrical energy • A battery is a source of emf in parallel with an internal resistance • Resistors in series: Summary of Chapter 19 • Resistors in parallel: • Kirchhoff’s rules: 1. sum of currents entering a junction equals sum of currents leaving it 2. total potential difference around closed loop is zero Summary of Chapter 19 • Capacitors in parallel: • Capacitors in series: Summary of Chapter 19 • RC circuit has a characteristic time constant: • To avoid shocks, don’t allow your body to become part of a complete circuit • Ammeter: measures current • Voltmeter: measures voltage