Learning Goals for this lecture

Transcription

1 Lecture 7 General Physics II Learning Goals for this lecture Be able to calculate the resistance, current, voltage, and power for the loads, resistors, and capacitors in a simple electric circuit. Understand that charging and discharging capacitors involves an exponential function, and why this is central to electronics. Basic familiarity with domestic wiring and AC electrical power.

2 ConcepTest 18.5a Lightbulbs Two lightbulbs operate at 120 V, but one has a power rating of 25 W while the other has a power rating of 100 W. Which one has the greater resistance? a) the 25 W bulb b) the 100 W bulb c) both have the same d) this has nothing to do with resistance

3 ConcepTest 18.5a Two lightbulbs operate at 120 V, but one has a power rating of 25 W while the other has a power rating of 100 W. Which one has the greater resistance? Lightbulbs a) the 25 W bulb b) the 100 W bulb c) both have the same d) this has nothing to do with resistance Since P = V 2 / R the bulb with the lower power rating has to have the higher resistance. Follow-up: Which one carries the greater current?

4 ConcepTest 18.5b Space Heaters I Two space heaters in your living room are operated at 120 V. Heater 1 has twice the resistance of heater 2. Which one will give off more heat? a) heater 1 b) heater 2 c) both equally

5 ConcepTest 18.5b Space Heaters I Two space heaters in your living room are operated at 120 V. Heater 1 has twice the resistance of heater 2. Which one will give off more heat? a) heater 1 b) heater 2 c) both equally Using P = V 2 / R, the heater with the smaller resistance will have the larger power output. Thus, heater 2 will give off more heat. Follow-up: Which one carries the greater current?

6 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, T C. Tc ~ 23 K for metals Even the co-called high-tc materials have Tc ~ 90 K Superconductors are used in MRI scanners to create extremely strong electromagnets

7 19.2 Resistors in Parallel A parallel connection splits the current; the voltage across each resistor is the same:

8 19.2 Resistors in Parallel The total current is the sum of the currents across each resistor: (19-4)

9 19.3 Kirchhoff s Rules Complicated circuits cannot be simply broken down into series and parallel connections. 1. Junction Rule: Sum of currents entering a junction equals the sum of currents leaving it. (Conservation of Charge) 2. Loop Rule: Sum of voltage drops around a closed path equals zero. (Conservation of Energy)

10 The sum of the changes in potential around a closed loop is zero. This is a restatement of the conservation of energy Think of the graph on the right as a rollercoaster Kirchhoff s Loop Rule

11 Circuit 1 Circuit 2 These circuit diagrams show two different ways of connecting the same battery and 3 resistors, R 1, R 2 & R 3. Which has the lower total resistance? A. Circuit 1 B. Circuit 2 C. Same

12 Circuit 1 Circuit 2 These circuit diagrams show two different ways of connecting the same battery and 3 resistors, R 1, R 2 & R 3. Which draws more Current from the battery? A. Circuit 1 B. Circuit 2 C. Neither

13 Using Kirchhoff s Rules Problem Solving: Kirchhoff s Rules 1. Label each current. 2. Identify unknowns. 3. Apply junction and loop rules; you will need as many independent equations as there are unknowns. 4. Solve the equations, being careful with signs.

14 Charging a Battery EMFs in series, opposite direction: total voltage is the difference, but the lower-voltage battery is charged. Rechargable batteries contain electrodes and chemicals whose redox reactions are reversible.

15 RC Circuits Resistor and Capacitor in Series - Very useful When the switch is closed, the capacitor will begin to charge. As you might expect, it takes a while. How long is a while? We can control precisely how long it takes by a setting the voltage across the capacitor

16 RC Time Constant - The(?) fundamental principle of Electronics Charge flows onto a capacitor rapidly at first, slowing down as it fills. Why? -The charges flowing into plate A are attracted by plate B, but are at the same time repelled by the other charges already in plate A. The rate at which the capacitor fills with charge is described by a math function called an Exponential (y=e x ) ΔQ = Q 0 e -t/τ Euler s number e = "

17 RC Circuits Just what is the Time Constant? The time constant τ is the amount of time it would take for the charge on the capacitor to change by a certain factor. In another exponential situation, radioactive decay, the chosen constant is called the half-life, or amount of time for half the radioactive atoms to decay. In electronics we can construct a physical property of the circuit that happens to have the dimension of time. The product of resistance and capacitance, RC has the units of seconds (can you prove it?) Handy Fact: It turns out that the charge stored in the capacitor changes by 63% in the time RC.

18 The voltage across the terminals of the capacitor follows a similar curve to the charge EMF ( curly E ) here is the voltage being supplied (usually by a battery) to the circuit. V c is the capacitor s voltage after charging for a time t in seconds.

19 A camera flash is to produce most its light in 1/500 sec, and the flash bulb has a resistance of 65 Ohms. What would be a good value for the capacitor? (Clicker) Answer in MicroFarads (µf)

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21 Discharging a Capacitor If an isolated charged capacitor is connected across a resistor (or a load, like a flash-bulb) it discharges exponentially. A flashbulb has a very small resistance (it draws a large current), so the capacitor will discharge very fast, which is what you need!

22 Alternating Current (AC) Chapter 18/19 Edison Westinghouse Niagara Falls War of the Currents How we came to use alternating current (AC) for electrical power supply. Tesla

23 Direct Current & Alternating Current Current from a battery flows steadily in one direction (direct current, DC). Current from a rotating turbine varies sinusoidally (alternating current, AC).

24 18.7 Alternating Current The voltage varies sinusoidally with time: as does the current: (18-7)

25 RMS Voltage and Current The AC current and voltage both have average values of zero, but the energy being transferred is always positive For example a lightbulb filament heats up the same amount no matter which way the current is flowing There is a simple math operation that can calculate the equivalent direct voltage and current. We first square the voltage (which makes the negative values positive), then take the average (which levels out the bumps),and finally take the square root (to undo the squaring) The result is called the root mean square (rms) voltage (and current) The RMS voltage is about 2/3 of the peak voltage, and the peak-to- peak voltage is double that. In the USA we use 110 volts RMS at 60 Hz Europe uses 230 volts RMS at 50 Hz

26 Power and Alternating Current Multiplying the current and the voltage gives the power: P = VI (just like for DC electricity) No so helpful. So we really want the time averaged value. Which can be written in terms of the load and peak voltage or load and peak current

27 Comparing Direct and Alternating Current DC Batteries naturally produce DC Resistance cross section (A) of wire Cannot be efficiently stepped up/ down. Circuits obey relatively simple rules Electricity is dangerous AC AC Generation is efficient and simple R complicated by the skin effect, and extra radiative losses Transformers readily convert voltage between high ( kv) for transmission and 120v for use. Complex, dynamic circuits, but obey the same rules, with some modifications. Additional risk to heart rhythm Charge flows though the circuit Charge oscillates back and forth (50/60 Hz)

28 Line Losses and High Voltage Transmission Wires have a resistance, so they dissipate power. This is called line loss P trans =VI is the total transmitted power P lost = I 2 R is the lost power. Why is power transported at high voltage? Transmitting 100 kw at domestic voltage (110v) P t1 = VI -> I = 100x10 3 / 110 = 909 A Transmitting 100 kw at 1100 volts (1.1 kv) P t2 = VI -> I = 100x10 3 / 1000 = 90.9 A P lost_1 = R P lost_2 = 90 2 R Stepping up the voltage (and hence stepping the current down), improves efficiency by the square of the change in voltage (or current). In this case raising V by a factor of 10, cut the line loss by a factor of 100! So: P lost_1 /P lost2 = 100 Long distance power lines (110kV) lose about 3% per 1000 km Local power lines are closer to 1% per mile

29 19.7 Electric Hazards A person receiving a shock has become part of a complete circuit. Even very small currents 10 to 100 ma can be dangerous, disrupting the nervous system. Larger currents may also cause burns. Your electrical resistance is about Ohms When wet: 10 3 Ohms or less Calculate for 120v!!!

30 19.7 Electric Hazards Faulty wiring and improper grounding can be hazardous. Make sure electrical work is done by a professional.

31 Domestic Wiring Remember, Domestic wiring uses alternating current (AC)! 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. You can get a shock from the neutral wire, it is not the same as ground!

32 Measuring Current, Voltage, and Resistance. An Ammeter measures current. (needs low R) A Voltmeter measures voltage. (needs high R) An Ohmmeter measures resistance. (needs a battery) Today all 3 functions are typically performed by a single instrument called a Multimeter Multimeters have a separate mode for AC, remember to use it!

33 Electro Motive Force (EMF) and Terminal Voltage Batteries have an internal resistance (r ), which behaves as though it were in series with the emf. So the terminal voltage drops when a load is applied. R is negligible only when Ir < amp.hr rating /10

34 Internal Resistance of Batteries As current flows from the battery, the voltage across its terminal falls. If the voltage drop is too great, the battery will not be able to produce enough power. Also since battery has its own resistance, it wastes or dissipates power according to P=I 2 R This is why your laptop battery scorches your leg, and why you can t start a car with a handful of AAA s Typically r = Ohms (higher for smaller cells) Battery Amp.hr rating AAA AA 1-2 C 4-8 D 8-12 Car