Electric Circuits Physics Unit 9 This Slideshow was developed to accompany the textbook OpenStax Physics Available for free at https:// openstaxcollege.org/textbooks/college-physics By OpenStax College and Rice University 2013 edition Some examples and diagrams are taken from the textbook.

Slides created by Richard Wright, Andrews Academy [email protected] 09-01 Current, Resistance, and Ohms Law Current Rate of flow of charge Amount of charge per unit time that crosses one point

Symbol: (I) Unit: ampere (A) 09-01 Current, Resistance, and Ohms Law Small computer speakers often have power supplies that give 12 VDC at 200 mA. How much charge flows through the circuit in 1 hour and how much energy is used to deliver this charge? = 720 C E = 8640 J

09-01 Current, Resistance, and Ohms Law Conventional Current Electrons are the charge that flows through wires Historically thought positive charges move Conventional current imaginary flow of positive charges Flows from positive terminal and into negative terminal Real current flows the opposite way

09-01 Current, Resistance, and Ohms Law Drift Velocity Electrical signals travel near speed of light, but electrons travel much slower Each new electron pushes one ahead of it, so current is actually like wave q = charge of each electron

n = free charge density A = cross-sectional area = drift velocity 09-01 Current, Resistance, and Ohms Law Think of water pumps Bigger pumps more water flowing Skinny pipes (more resistance) less water flow Electrical Circuits Bigger battery voltage more current

Big electrical resistance less current 09-01 Current, Resistance, and Ohms Law Ohms Law V = emf I = current R = resistance Unit: V/A = ohm ()

09-01 Current, Resistance, and Ohms Law Resistors Device that offers resistance to flow of charges Copper wire has very little resistance Symbols used for Resistor Wire

09-01 Current, Resistance, and Ohms Law Our speakers use 200 mA of current at maximum volume. The voltage is 12V. The current is used to produce a magnet which is used to move the speaker cone. Find the resistance of the electromagnet. R = 60 09-01 Homework Hopefully these circuit problems wont have you

running around in circles Read 20.3 09-02 Resistance and Resistivity Another way to find resistance The resistance varies directly with length and inversely with width (or cross-sectional area) a wire Kind of like trying to get a lot of water through a pipe Short, thick wire small resistance Long, skinny wire large resistance

09-02 Resistance and Resistivity = resistivity Unit: m Table 20.1 lists resistivities of some materials Metals small resistivity (1x10-8 m) Insulators large resisitivity (1x1015 m)

Semi-conductors medium resistivity 09-02 Resistance and Resistivity Why are long wires thick? Wire thicknesses are measured in gauges. 20-gauge wire is thinner than 16-gauge wire. If 20-gauge wire has and 16-gauge wire has , find the resistance per meter of each if they are copper. 20-guage 16-guage

09-02 Resistance and Resistivity Resistivity and Temperature = resistivity at temperature T = resistivity at temperature T0 = temperature coefficient of resistivity Unit: 1/C (or 1/K) 09-02 Resistance and Resistivity

Metals Resistivity increases with temperature is positive Semiconductors Resistivity decreases with temperature is negative 09-02 Resistance and Resistivity Resistance and Temperature

R = resistance at temperature T R0 = resistance at temperature T0 = temperature coefficient of resistivity Unit: 1/C (or 1/K) 09-02 Resistance and Resistivity A heating element is a wire with cross-sectional area of and is 1.3 m long. The material has resistivity of at 200C and a temperature coefficient of 1/C. Find the resistance of the element at 350C.

R = 1430 09-02 Resistance and Resistivity Superconductors Materials whose resistivity = 0 Metals become superconductors at very low temperatures Some materials using copper oxide work at much higher temperatures No current loss Used in Transmission of electricity

MRI Maglev Powerful, small electric motors Faster computer chips 09-02 Homework Resistance is futile Read 20.4, 20.5 09-03 Electric Power and AC/DC

W P t W EPE q V q V P t

q I t P IV 09-03 Electric Power and AC/DC Power

Unit: Watt (W) Other equations for electrical power 09-03 Electric Power and AC/DC Lets say an electric heater has a resistance of 1430 and operates at 120V. What is the power rating of the heater? How much electrical energy does it use in 24 hours? P = 10.1 W E = 873 kJ

09-03 Electric Power and AC/DC Kilowatt hours Electrical companies charge you for the amount of electrical energy you use Measured in kilowatt hours (kWh) If electricity costs $0.15 per kWh how much does it cost to operate the previous heater (P = 10.1 W) for one month? $1.09

09-03 Electric Power and AC/DC Alternating Current Charge flow reverses direction periodically Due to way that power plants generate power Simple circuit 09-03 Electric Power and AC/DC Periodicity Voltage, Current, and Power fluctuate with time

So we usually talk about the averages 09-03 Electric Power and AC/DC Average Power DC AC Often P is used to represent average power in all AC circuits.

09-03 Electric Power and AC/DC Root Mean Square (rms) and are called root mean square current and voltage Found by dividing the max by 09-03 Electric Power and AC/DC Convention in USA V0 = 170 V

Vrms = 120 V Most electronics specify 120 V, so they really mean Vrms We will always (unless noted) use average power, and root mean square current and voltage Thus all previously learned equations work! 09-03 Electric Power and AC/DC A 60 W light bulb operates on a peak voltage of 156 V. Find the Vrms, Irms, and resistance of the light bulb. Vrms = 110 V

Irms = 0.55 A R = 202 09-03 Electric Power and AC/DC Why are you not supposed to use extension cords for devices that use a lot of power like electric heaters? P = IV P is large so I is large The wire has some resistance

The large current and little resistance can cause heating If wire gets too hot, the plastic insulation melts 09-03 Homework Dont write down just answers. Alternatively show your work, too. Read 20.6, 20.7 09-04 Electricity and the Human Body

Thermal Hazards Electric energy converted to thermal energy faster than can be dissipated Happens in short circuits Electricity jumps between two parts of circuits bypassing the main load

Low R so high P Can start fires Circuit breakers or fuses try to stop Or long wires that have High resistance (thin) Or are coiled so heat cant dissipate 09-04 Electricity and the Human Body

Shock Hazards Factors Amount of Current Path of current Duration of shock Frequency of current Human body mainly water, so decent conductor Muscles are controlled by

electrical impulses in nerves A shock can cause muscles to contract Cause fist to close around wire (muscles to close, stronger than to open) Can cause heart to stop Body most sensitive to 50-60 Hz 09-04 Homework

Dont let these problems shock you. Read 21.1 09-05 Resistors in Series and Parallel Series Wiring More than one device on circuit Same current through each device Break in device means no current

Form one loop The resisters divide the voltage between them 09-05 Resistors in Series and Parallel V divide among resistors V = V1 + V2 + V3 V = IR V = IR1 + IR2 + IR3 V = I(R1 + R2 +R3)

V = IRS RS = R1 + R2 + R3 + 09-05 Resistors in Series and Parallel A 5.17 k resistor and a 10.09 k resistor are connected in series. What is the equivalent resistance? 15.26 k 09-05 Resistors in Series and Parallel Bathroom vanity lights are occasionally wired in series. V = 120 V

and you install 3 bulbs with R = 8 and 1 bulb with R = 12. What is the current, voltage of each bulb, and the total power used? I = 3.33 A V = 26.7 V, 40 V Ptotal = 400 W 09-05 Resistors in Series and Parallel Parallel Wiring Same voltage across several

devices Typical house wiring Break in device has no effect on current Resistors divide current 09-05 Resistors in Series and Parallel Derivation Each branch draws current as if the other wasnt there Each branch draws less current than the power supply gives

R=V/I Overall circuit: Large I Small R Smaller resistance than either branch 09-05 Resistors in Series and Parallel I I1 I 2 V V I

R1 R2 1 1 1 V I V

R2 R1 RP V I R 09-05 Resistors in Series and Parallel

Parallel Resistors 09-05 Resistors in Series and Parallel A 1004 resistor and a 101 resistor are connected in parallel. What is the equivalent resistance? 91.8 If they were connected to a 3 V battery, how much total current would the battery supply? 32.7 mA

How much current through each resistor? 3.0 mA and 29.7 mA 09-05 Resistors in Series and Parallel Circuits Wired Partially in Series and Partially in Parallel Simplify any series portions of each branch Simplify the parallel circuitry of the branches If necessary simplify any remaining series 09-05 Resistors in Series and Parallel

Find the equivalent resistance and the total current of the following circuit. 101 5.17 k 10.09 k

100.9 k 3V 1004 09-05 Resistors in Series and Parallel Find the equivalent resistance. 5.17 k 10.09 k

3V 100.9 k 1004 101 09-05 Homework These series of problems

parallel the lesson. Read 21.2 09-06 Electromotive Force: Terminal Voltage Emf Electromotive force Not really a force Really voltage produced that could drive a current 09-06 Electromotive Force: Terminal Voltage

Internal Resistance Batteries and generators have resistance In batteries due to chemicals In generators due to wires and other components Internal resistance is connected in series with the equivalent resistance of the circuit 09-06 Electromotive Force: Terminal Voltage Internal resistance causes terminal voltage to drop below emf

Internal resistance is not necessarily negligible terminal voltage emf current of circuit

internal resistance 09-06 Electromotive Force: Terminal Voltage A string of 20 Christmas light are connected in series with a 3.0 V battery. Each light has a resistance of 10 . The terminal voltage is measured as 2.0 V. What is the internal resistance of the battery? 100 09-06 Electromotive Force: Terminal Voltage

A battery has an internal resistance of 0.02 and an emf of 1.5 V. If the battery is connected with five 15 light bulbs connected in parallel, what is the terminal voltage of the battery? 1.49 V 09-06 Electromotive Force: Terminal Voltage If batteries are connected in series, their emfs add, but so do the internal resistances If batteries are connected in

parallel, their emfs stay the same, but the currents add and the combined internal resistance is less 09-06 Homework Hard work takes lots of emf! Read 21.3 09-07 Kirchhoffs Rules

Kirchhoffs Rules Junction Rule Total current into a junction must equal the total current out of a junction Loop Rule For a closed-circuit loop, the total of all the potential rises total of all potential drops = 0 (or the total voltage of a loop is zero)

09-07 Kirchhoffs Rules Reasoning Strategy Draw the current in each branch of the circuit (flows out of positive terminal of battery). Choose any direction. If you are wrong you will get a negative current. Mark each element with a plus and minus signs at opposite ends to show potential drop. (Current flows from + to through a resistor) If the current leaves the element at +, voltage rise If the current leaves the element at -, voltage drop

Apply junction rule and loop rule to get as many independent equations as there are variables. Solve the system of equations. 09-07 Kirchhoffs Rules Find the current through the circuit 10.09 k 1004

4.5 V 3V 5.17 k 101 09-07 Kirchhoffs Rules Find the currents through each

element. 100.9 k I1 I2 101 1004

I3 3V 5.17 k 4.5 V 10.09 k 09-07 Homework

Currently, you need to work on these problems Read 21.4 09-08 DC Voltmeters and Ammeters Analog (non-digital) meters Main component galvanometer 09-08 DC Voltmeters and Ammeters

Ammeters Measures current Inserted into circuit so current passes through it Connected in series 09-08 DC Voltmeters and Ammeters Coil usually measures only little current

Has shunt resistors connected in parallel to galvanometer so excess current can bypass A knob lets you select which shunt resistor is used 09-08 DC Voltmeters and Ammeters Problems with Ammeters The resistance of the coil and shunt resistors add to the

resistance of the circuit This reduces the current in the circuit Ideal ammeter has no resistance Real-life good ammeters have small resistance so as only cause a negligible change in current 09-08 DC Voltmeters and Ammeters Voltmeters Connected in parallel to circuit since parallel has same voltage

The coil works just like in the ammeter Given the current and the resistance of the coil V = IR To give more range, a large resistor is connected in series with the coil 09-08 DC Voltmeters and Ammeters Problems with Voltmeters

The voltmeter takes some the voltage out of the circuit Ideal voltmeter would have infinitely large resistance as to draw tiny current Good voltmeter has large enough resistance as to make the current draw (and voltage drop) negligible 09-08 Homework See if you measure up to these meter problems Read 21.6

09-09 DC Circuits Containing Resistors and Capacitors Charging a Capacitor Circuit with a capacitor, battery, and resistor Initially capacitor is uncharged When battery connected current flows to charge capacitor As charges build up, there is increased resistance because of the repulsion of

the charges on the parallel plates When capacitor is fully charged, no current will flow 09-09 DC Circuits Containing Resistors and Capacitors Loop Rule Solve for I I is rate of change of q Differential Calculus says

09-09 DC Circuits Containing Resistors and Capacitors Charging a Capacitor RC = (time constant The time required to charge the capacitor to 63.2%)) CV = Q (maximum charge)

Where V is voltage across the capacitor is emf t is time R is resistance of circuit C is capacitance 09-09 DC Circuits Containing Resistors and Capacitors

Discharging a Capacitor The battery is disconnected The capacitor acts like a battery supplying current to the circuit Loop Rule Often capacitors are used to

charge slowly, then discharge quickly like in camera flash. Done by have different values for R in charging and discharging. 09-09 DC Circuits Containing Resistors and Capacitors Camera flashes work by charging a capacitor with a battery. Usually has a large time

constant because batteries cannot produce charge very fast The capacitor is then discharged through the flashbulb circuit with a short time constant 09-09 DC Circuits Containing Resistors and Capacitors An uncharged capacitor and a resistor are connected in series to a battery. If V = 12 V, C = 5 F, and R = 8105 . Find the time

constant, max charge, max current, and charge as a function of time. 09-09 Homework Discharge your knowledge by completing these problems