Lesson 18 Electric Current Eleanor Roosevelt High School Chin-Sung Lin

Flow of Charge and Electric Circuits

Water Flow Model High Potential Energy Water Water Pipe Height Water Doing Work Pump Doing Work Low Potential Energy Water

Water Flow vs. Electric Current High Potential Energy Water Water Pipe Height Water Doing Work Pump Doing Work Low Potential Energy Water

Electric Current Model High Voltage Electric Circuits Voltage Electric Current Doing Work Battery Doing Work Low Voltage

Water / Electric Current Model

Electric Current Model High Voltage Electric Circuits Voltage Electric Current Doing Work Battery Doing Work Low Voltage

Electric Current Model High Voltage Electric Circuits Electric Current Doing Work Battery Doing Work Voltage Low Voltage

Light Bulb Structure

Electric Circuit Symbols Wire Resistor Battery Voltage

Electric Circuits Wire Battery Resistor

Electric Circuits

Ohm’s Law

Electric Current Current (I) Voltage (V) Resistance (R)

Electric Current I (amperes , A) V (volts, V) R (ohms, Ω)

Ohm’s Law V I R

Ohm’s Law V: Voltage (V) I : Current (A) R: Resistance (Ω)

Voltmeter – Measuring Voltage

Ammeter – Measuring Current

Multimeter – Measuring All V: Voltage (V) I : Current (A) R: Resistance (Ω)

Digital Multimeter – Measuring All V: Voltage (V) I : Current (A) R: Resistance (Ω)

Digital Multimeter – Measuring All

Digital Multimeter – Measuring All Voltage / Resistance Current Ground

Digital Multimeter – Measuring All

Digital Multimeter – Measuring All Resistance DC Voltage AC Voltage DC Current AC Current Transistor

Ohm’s Law A V (V) I (A) R (Ω) V

Ohm’s Law

voltage = constant x current V = R x I Ohm’s Law voltage = constant x current V = R x I V: Voltage (V) I : Current (A) R: Constant or Resistance (Ω)

Ohm’s Law R = or V = I R or I = V R I V: Voltage (V) I : Current (A) R: Resistance (Ω)

Ohm’s Law Example What is the current through a 4-ohm resistor connected to a 12-V power supply?

Ohm’s Law Example What is the current through a 4-ohm resistor connected to a 12-V power supply? I = V / R I = 12 V / 4 Ω = 3 A

Ohm’s Law Example A 5-ohm resistor has a 8-A current in it. What is the voltage across the resistor?

Ohm’s Law Example A 5-ohm resistor has a 8-A current in it. What is the voltage across the resistor? V = I R V = 8 A x 5 Ω = 40 V

Ohm’s Law Example What is the resistance of a device that uses 2.5 A of current when connected to a 15-volt power source?

Ohm’s Law Example What is the resistance of a device that uses 2.5 A of current when connected to a 15-volt power source? R = V / I R = 15 V / 2.5 A = 6 Ω

Ohm’s Law Exercises What is the current through a 6-KΩ resistor connected to a 9-V power supply? What is the resistance of a device that uses 0.5 mA of current when connected to a 5-volt power source? A 2.5-MΩ resistor has a 0.02-mA current in it. What is the voltage across the resistor?

Resistors

Resistors A resistor is a two-terminal electronic component which implements electrical resistance Resistors are used to control the amount of current flowing in a circuit Resistor are usually measured by the units of Ω, kΩ, and MΩ

Resistors

Resistors on PCB

Resistor Color Coding

Surface Mount Resistors

SMT Resistors on PCB

Resistance and Resistivity

Resistance Electric current in a circuit is decided by voltage (V) and resistance (R): I = V / R What are the factors to determine the resistance?

Resistance & Length Which one has larger resistance?

Resistance & Length Which one has larger resistance?

Resistance & Length Which one has larger resistance? R ~ L

Resistance & Area Which one has larger resistance?

Resistance & Area Which one has larger resistance?

Resistance & Area Which one has larger resistance? R ~ 1 A

Resistance & Resistivity Which one has larger resistance? Copper Silver

Resistance & Resistivity Which one has larger resistance? Copper Silver

Resistance & Resistivity of Materials

Resistance & Resistivity Which one has larger resistance? Copper Silver R ~ ρ

Resistance ρ L R = A Resistance is determined by ρ resistivity [Ω m] L length [m] A cross-section area [m2] R = ρ L A

Resistance Example A 0.5-m long Nichrome wire has 0.001 m2 cross-section. What is the resistance of the wire?

Resistance Example A 0.5-m long Nichrome wire has 0.001 m2 cross-section. What is the resistance of the wire? R = ρ L / A = (150 x 10 -8 Ωm) (0.5 m) / 0.001 m2 = 7.5 x 10-4 Ω

Resistance Exercise A 1.2 x 10-5 Ω Copper wire has 0.004 m2 cross- section. What is the length of the wire?

Resistance Exercise A 1.2 x 10-5 Ω Copper wire has 0.004 m2 cross- section. What is the length of the wire? R = ρ L / A 1.2 x 10-5 Ω = (1.72 x 10 -8 Ωm) L / 0.004 m2 L = 2.79 m

Electric Current

Electric Current Electric current is the flow of charge In solid conductors: the electrons In fluids: positive and negative ions as well as electrons Electric current is usually measured in units of A and mA

Electric Current When electrons flow in a wire, the number entering one end is the same as the number leaving the other The net charge of the wire is normally zero

Electric Current Electric (conventional) current is from positive to negative, while electron flow is from negative to positive

Electric Current Current is the charge flow rate past a given cross-section (current) = (charge) / (time) or I = Q / t

Electric Current 1 A is 1 C of charge going past a given cross-section per second 1 C is 6.24 x 1018 electrons

Electric Current Example How much current must there be in a circuit if 100 coulombs flow past a point in the circuit in 4 seconds?

Electric Current Example How much current must there be in a circuit if 100 coulombs flow past a point in the circuit in 4 seconds? I = Q / t = 100 C / 4 s = 25 A

Electric Current Exercise If there is a current of 20 amperes in a circuit for 10 minutes, what quantity of electric charge flows in through the circuit? 


Electric Current Exercise If there is a current of 20 amperes in a circuit for 10 minutes, what quantity of electric charge flows in through the circuit? Q = I t = 20 A x 600 s = 12000 C 


Electric Current Exercise How much time is required for 10 coulombs of charge to flow past a point if the rate of flow (current) is 2 amperes?

Electric Current Exercise How much time is required for 10 coulombs of charge to flow past a point if the rate of flow (current) is 2 amperes? t = Q / I = 10 C / 2 A = 5 s

Voltage Sources

Voltage Source A voltage source is a two-terminal circuit element which supplies a constant DC or AC potential difference for any current flow through it Voltage sources: dry cell batteries, wet cell batteries, solar panel, or generators Voltages are usually measured by the units of V, kV, and MV

Voltage Source The potential energy per coulomb of charge available to electrons moving between terminals is the voltage V = W / q Voltage is sometimes called the electromotive force, or emf

Voltage Sources: Dry Cell

Voltage Sources: Wet Cell

Voltage Sources: Solar Panel

Voltage Sources: Generator

Batteries in Parallel / Series

Batteries in Parallel / Series

Batteries in Parallel / Series Exercise Calculate the current in each case 1 KΩ

Electric Shock

Electric Shock The damaging effects are the result of current passing through the body The current depends on the voltage applied and also on the resistance of the human body (I = V / R) The resistance of the body range from ~100 Ω to ~500 KΩ

Electric Shock Current (A) Effect 0.001 can be felt 0.005 painful 0.010 involuntary muscle contractions (spasms) 0.015 loss of muscle control 0.070 if through the heart, serious disruption; probably fatal if current lasts for more than 1 second

Electric Shock Why do the birds perch on the high- voltage wires not getting electric shock?

Electric Shock Why do the birds perch on the high- voltage wires not getting electric shock? Because every part of their bodies is at the same high potential as the wire

DC & AC

Direct Current (DC) A flow of charge that flows in one direction, even if the current moves in unsteady pulses A battery produces direct current Electrons always move through the circuit in the same direction from the negative terminal and toward the positive terminal

Direct Current (DC)

Direct Current (DC) Waveform Time Voltage Voltage Time

Alternating Current (AC) A flow of charge is alternating its directions This is accomplished by alternating the polarity of voltage at voltage source

Alternating Current (AC)

Alternating Current (AC) Waveform Voltage Time Voltage Time

Alternating Current (AC) Nearly all of the commercial AC circuits in North America involves 120 V and 60 Hz Europe adopted 220 V as their standard

Alternating Current (AC) The 120 V refers to the “root-mean-square” (RMS) average of the voltage The actual voltage in a 120 V AC circuit varies between +170 V and – 170 V peaks. It delivers the same power as a 120 V DC circuit

Alternating Current (AC) Because most electric service in the United States is three-wire: one wire at +120 V, one wire at 0 V (neutral), and the other wire at -120 V Most of the appliance use +120V/-120 V and the neutral wires, producing 120 V. When use both +120V and -120 V wires, a 240 V is produced

AC-to-DC Conversion

Speed of Electrons

Thermal Speed vs. Drift Speed

Thermal Speed vs. Drift Speed Thermal motion (random motion) speed inside a metal wire is about 1/200 the speed of light Under electric field, the Drift Speed (net speed) is only about 0.01 cm/s

Speed of Electrons The electrons will collide with the metallic ions in their path and transfer some kinetic energy to them The extremely high speed of electricity is not due to the electrons but due to the signal. The signal is traveling at near high speed

Speed of Electrons The electrons inside the conductor will shift forward (DC) or forward and backward (AC) Why does the electric power company charge you money when they provide you AC electricity which no net electrons enter your home?

Speed of Electrons The AC outlets in your home do not supply you electrons but supply you energy The source of the electrons is the conducting circuit material itself

Electric Power

Electric Power The rate at which electrical energy is converted into another form (mechanical energy, heat, or light) is called electric power (Electric Power) = (Electric Energy) / (Time) Unit: Watts (W) P = W t

Electric Power P = I V P = = V I = I V t = q W Electric Power = Energy / Time = (Charge/Time) x (Energy/Charge) = Current x Voltage Unit: 1 watt = (1 ampere) x (1 volt) P = = V I = I V W t = q P = I V

Electric Power Derive the formulas of P, I, R, P, V, R

Electric Power P = I V = I (I R) = I 2 R P = I V = ( ) V = P = I V = I 2 R = V 2 R

Electric Power W = P t Since Energy / Time = Power, Energy = Power x Time Derive the formulas of W, I, V, and t W, I, R, and t W, V, R and t W = P t

Electric Power W = P t = I V t = I 2 R t W = P t = I V t = ( ) t = t Since Energy/Time = Power, so Energy = Power x Time W = P t = I V t = I 2 R t W = P t = I V t = ( ) t = t V 2 R W = Pt = IVt = I2Rt = t V 2 R

Electric Power Energy can be represented in units of kilowatt-hours (kW·h) 1 kW·h = 3.6 x 106 J A kilowatt is 1000 watt, and a kilowatt- hour is the energy consumed in 1 hour at the rate of 1 kilowatt

Electric Power Example A light bulb is plugged into a 120-volt outlet and has a 0.7 A current in it. What is the power rating of the light bulb?

Electric Power Example A light bulb is plugged into a 120-volt outlet and has a 0.7 A current in it. What is the power rating of the light bulb? P = I V = (0.7 A)(120 V) = 84 W

Electric Power Example A heater uses 21 A when connected to a 110-V line. If electric power costs 10 cents per kilowatt-hour in this location, what is the cost of running the heater for 13 hours?

Electric Power Example A heater uses 21 A when connected to a 110-V line. If electric power costs 10 cents per kilowatt-hour in this location, what is the cost of running the heater for 13 hours? W = I V t = (21 A)(110 V)(13 hr) = 30030 W-hr = 30.03 kW-hr Cost = ($ 0.1 /kW-hr)(30.03 kW-hr) = $3.00

Electric Power Exercise A 120 V outlet in Tony’s house is wired with a circuit breaker on an 8 A line. a) If Tony tries use his newly-bought 1200-Watt hair dryer, will he trip the circuit breaker? b) What is the resistance of the hair dryer?

Electric Power Exercise Alice likes to keep her 40-Watt front porch light on at night time from 10 p.m. to 6 a.m., and Alice pays 8.00¢ per kWh, how much does it cost to run the light for this amount of time each week?

The End