Unit 2: Electricity and Magnetism Lesson 3: Simple Circuits Electric circuits transfer energy. Electrical energy is converted into light, heat, sound, mechanical work, etc. The byproduct of any circuit is always heat. Circuit: Closed loop of moving charges (electrons move - flow of negative charges; positive ions move - flow of positive charges. Nucleus not moving) Voltage: The amount of work that each charge will do as it goes through the circuit. It is the amount of push on the charges. (SI unit V - volt) Voltmeter: Instrument used to measure voltage change between 2 points in a circuit. They have very high resistance so that the current flow through them is a minimum. A voltmeter is always connected in parallel with the part of the circuit for which you wish to measure voltage. Voltmeters are connected positive to negative, and negative to positive. Current: (electron current) Flow of charged particles - the rate of flow of charges - Charge/sec, C/s (SI unit A - Ampere) symbol I Ammeter: Instrument used to measure current through a branch of an electric circuit. Ammeters have very low resistance so that the current flow through them is a maximum. An ammeter is always connected in series with the branch through which you wish to measure current. Ammeters are 1
connected positive to positive and negative to negative. Conventional Current: Flow of positive charge in circuit - defined before we knew that electrons were responsible for flow of electricity (positive charge moves - not nuclei) Conventional current flows from high potential to low potential. Electromagnetism: When electrons flow in a circuit, they create a magnetic field (static charges create only electric fields). Resistance: The opposition to the flow of charge. Any appliance that asks the charge to do work will slow it down. (SI unit Ω, ohm) 1 Ω = 1 V/ 1 A An electron traveling through the wires and loads of the external circuit encounters resistance. Resistance is the hindrance to the flow of charge. For an electron, the journey from terminal to terminal is not a direct route. Rather, it is a zigzag path that results from countless collisions with fixed atoms within the conducting material. The electrons encounter resistance - a hindrance to their movement. While the electric potential difference established between the two terminals encourages the movement of charge, it is resistance that discourages it. The rate at which charge flows from terminal to terminal is the result of the combined effect of these two quantities. The free electrons in a conductor behave like molecules in an ordinary gas. They move quickly and randomly, colliding with each other and with the atoms. When an electric field is applied across a conductor, in addition to the rapid random motion, the electrons drift very slowly (about 10-5 m/s) towards the positive end. This is the electron gas model. 2
Factors That Affect Resistance Resistance of a solid conductor depends upon: 1. resistivity of the material (ρ - Ω cm) 2. length of the conductor (L - m, meters, must change to cm) 3. cross-sectional area of the conductor (A, cm 2 ) 4. temperature The resistance, R, of a material of length, L, and cross-sectional area, A, is given by: What happens to R (assume ρ is a constant): As you increase A? As you increase L? Examples: (use resistivity table) 1. Calculate the resistance of a 24 Gauge, Cu wire, 6.5 m long. 2. Calculate the resistance of an 18 Gauge, Ag wire, 50 m long. 3
Resistivity: Inherent property of the material. Its unit is Ω cm or Ω m. Insulators have high resistivity (low conductivity). Conductors have low resistivity (high conductivity). Superconductivity & Critical temperature: Temperature below which resistivity of a class of materials goes to zero. Below the critical temperature, these materials offer no resistance to electric current. Once a current is established in a superconducting material below its critical temperature, it continues indefinitely with no need of an outside voltage source. Metals superconduct at temperatures slightly above absolute zero. http://www.superconductors.org/uses.htm The Simple Circuit A simple circuit contains the minimum things needed to have a functioning electric circuit. A simple circuit requires 3 things: 1. A source of electrical potential difference or voltage (typically a battery or electrical outlet) 2. A conductive path which would allow for the movement of charges (wire) 3. An electrical resistance (resistor) which is loosely defined as any object that uses electricity to do work (a light bulb, electric motor, heating element, speaker, etc.) 4
battery or source: escalator - raises charges to a higher level of energy. resistor: paddle wheel - As charges move through the circuit, they do work on the resistor and as a result, they lose energy. By the time each charge makes it back to the battery, it has lost all the energy given to it by the battery. As the charges move through a wire, they lose no energy (assuming the wires are short and are a good conductor). The potential drop ( - potential difference) across the resistor is the same as the potential rise( + potential difference) across the battery. The charges are positive so this is a representation of Conventional Current (the apparent flow of positive charges) The charges are only flowing in one direction so this would be considered direct current (D.C. ). Draw a simple circuit show conventional current direction and electron current direction. Short Circuit: A circuit with a battery and a wire leading from positive to negative terminal without an electrical device (light bulb, beeper, motor, etc.) would lead to a high rate of charge flow. Such a circuit is referred to as a short circuit. With charge flowing rapidly between terminals, the rate at which energy would be consumed would be high, and the wires get heated to a high temperature. 5
Ohm's Law describes mathematically the relationship between current and voltage (potential difference). The more potential difference you have the greater your current is going to be. The more resistance a circuit has, the lower the current is going to be. The following equation is Ohm's Law. It holds true for any circuit as long as temperature does not change. Ohm s law 1. Find the resistance of an electric light bulb if there is a current of 0.8 A and a potential difference of 120 V. Ans: 150 Ω 2. An 8 Ω resistor, a switch, and a 12 V battery are connected in a circuit. Draw the circuit diagram. Calculate the current. 6
3. A 541-Watt toaster is connected to a 120-V household outlet. What is the resistance of the toaster? Electric power (Joules Law) Joule experimentally determined the relationship between thermal energy and current flow. Power = rate of doing work = Joules/sec. Power = P = W t Work done on charge Time Power is the rate at which electrical energy is supplied to a circuit or consumed by a load. Power = Energy Consumed by Load Time A 60-watt light bulb - 60 joules of energy delivered to the light bulb every second. The ratio of the energy delivered or expended by the device to time is equal to the wattage of the device. Calculating Power: We can show that electric power is the product of the electric potential difference and the current. Power is the rate at which energy is added to or removed from a circuit by a battery or a load. Current is the rate at which charge moves past a point on a circuit. 7
Electric potential difference across the two ends of a circuit is the potential energy difference per charge between those two points. Combining equations, ΔPE = ΔV.Q Equations for Electric Power: 1. Power (P), Voltage (V), Current (I) 2. Power (P), Voltage (V), Resistance (R) 3. Power (P), Current (I), Resistance (R) Examples: 1. Given a resistance of 5 ohms and a current of 10 amperes, what power is dissipated in the circuit? 8
2. A 12 V battery is connected in a circuit. An ammeter reads 2 A. What resistance is connected in the circuit? What power is dissipated in the circuit? 3. Calculate the resistance and the current of a 7.5-Watt night light bulb plugged into a US household outlet (120 V). 4. The sticker on a compact disc player says that it draws 288 ma of current when powered by a 9 Volt battery. What is the power (in Watts) of the CD player? 5. The box on a table saw indicates that the amperage at startup is 15 Amps. Determine the resistance and the power of the motor during this time. Electrical Energy Power companies supply our electrical energy. Examples: 9
1. A 12 V battery is connected in a circuit. An ammeter reads 2 A. What resistance is connected in the circuit? What power is dissipated in the circuit? What electrical energy is used after 4 sec? 2. If a 120 V battery is connected in a circuit, and the ammeter reading is 1.5 A, what power is dissipated in the circuit? What resistance is connected in the circuit? What electrical energy is used after 3 minutes? 3. A 6 V battery delivers 0.5 A of current to an electric motor. What power is dissipated by the motor? How much electrical energy does it use in 5 min? Ans: 3 W; 900 J 4. A steam iron draws 6.0 A when connected to a potential difference of 120 V. a. What is the power rating of this iron? b. How many joules of energy are produced in 20.0 min. c. How much does it cost to run the iron for 20.0 min at 0.010/kWh? 5. You leave your 75 W light on for 2 weeks while you are on vacation. If the voltage is 120 V, calculate the current. How much does it cost you to run the light if electricity costs $.15 / Kwh? 6. A small electric furnace that expends 2.00 kw of power is connected across a potential difference of 120.0 V. a. What is the current in the circuit? b. What is the resistance of the circuit? c. What is the cost of operating the furnace for 24.0 h at 7.00 cents/kwh? 10
7. An 11.0 W energy-efficient fluorescent lamp is designed to produce the same illumination as a conventional 40.0 W lamp. a. How much energy does this lamp save during 100.0 hours of use? b. If electrical energy costs $0.080/kWh, how much money is saved in 100.0 hours? 11