Current Electricity Parallel Circuit Series Circuit

What You Will Learn Transfer of energy in circuits. Conversion of energy. Electric Current – Conventional vs. Flow of Electrons Resistance and Ohm’s Law Basic Circuits

What You Already Know You flip a switch to turn on a light, TV or computer. To turn on the car, you turn the ignition switch. MP3 players, cell phones and flashlights have on/off switches and use batteries. In each of these cases, you have a closed circuit in which electricity flows.

What You Already Know Charge by Conduction – The process by which electrons are transferred from one object to another because of differences in excess number of electrons on one surface compared to the other.

What You Already Know - Electric Potential the Electric Potential Difference is equal to the Work required to move a test charge in an electric field divided by the magnitude of the test charge. + ++++ - ---- A B qo F is constant since the electric field is constant from one plate to the other. F = qoE Uniform Electric Field Vtotal = W/qo = Fd/qo = Ed

Creating a Circuit Plate with excess number of electrons + ++++ - ---- Two equal and oppositely charged plates Plate with deficiency of electrons What would happen if a conductor was connected to both plates?

+ - + - + -+ - + - + - + - + - + - + - + - + - Creating a Circuit The electrons would flow from the negatively charged plate to the positively charged plate until the amount of charge was the same for both plates and the wire. Conventional Current Flow + - _ + - + - + -+ - + - + - + - + - + - + - + - + - + ++++ - ---- - - - - - - Electron Flow How do we maintain the flow of charge?

Creating a Circuit Charge pump Circuit: + ++++ - ---- Charge pump Battery Generator Gas/Oil Nuclear Hydro Wind Tidal Solar Electron Flow Electron Flow Circuit: A closed loop in which electric current can flow. It generally includes a device such as a light bulb that reduces the electric potential energy. It also includes a device to increase potential energy (Charge Pump).

I = q/t = 1 Coulomb/second = 1 Ampere (A) What is Current? Current is the rate of flow of charge. I = q/t = 1 Coulomb/second = 1 Ampere (A) Conventional Current = flow of positive charge. (Note that positive charges do NOT flow in metallic conductors.) Electron flow is simply the flow of electrons.

Ohm’s Law German Georg Simon Ohm discovered that the ratio of the potential difference to current is a constant for a given conductor. R = V/I Where: R = Resistance in Ohms () V = Electric Potential in Volts (V) I = Current in Amperes (A) Resistance is the hindrance to the flow of charge. Most metallic conductors obey Ohm’s Law.

Ohm’s Law The resistance (R) represents the slope (m) of a curve where V is plotted against I. What is R? For Ohmic materials, the curve is a straight line. 10 m = R = V/I Non-Ohmic e.g. light bulb

Examples: Ohm’s Law How much current flows through a 12 flashlight bulb operating at 3.0 volts? What is the voltage drop in a 5 resistor that has 2 amperes of current running through it? What is the resistance of a heating element in a toaster operating at 120 volts with a current flow of 2 amperes?

What causes resistance? E-field in conductor (resistor) is provided by a battery or voltage source. Charges (electrons) are put in motion due to influences of the electric field, but scatter in a very short time from things that get in the way defects, lattice vibrations (phonons), etc The more collisions, the greater the resistance and the fewer the collisions, the less the resistance. Imagine the following two scenarios. Running down the hallway in between periods Running down the hallway after the late bell when there is nobody in them. Under which scenario would you experience less resistance?

Resistivity & Resistance Resistivity is a measure of the conductive ability of the material. Resistivity is an intrinsic (natural) property of a material. The higher the resistivity, the higher the resistance and vice versa. For a conductor of length L (m) and cross-sectional area A (m2), the resistance can be determined by: R = L/A Where  = resistivity (•m) L = length of the conductor A = Cross-Sectional Area

Ex.: Resistance & Resistivity What would happen to the resistance in a wire if the length were increased? It would decrease. It would increase. It would remain the same. What would happen to the resistance in a wire if the cross-sectional area were increased? What would happen to the resistivity the length were increased?

Low Resistance vs. High Resistance To Summarize: Short fat wires make good conductors. While long skinny wires make poor conductors. I Short & Fat = Low Resistance I Long & Skinny = High Resistance

Resistance vs. Length and Resistance vs. X-Sectional Area What is the relationship between: Resistance and Length? Resistance and X-Sectional Area? Length Resistance X-Sectional Area Resistance

Resistivity vs. Temperature Note: The Resistivity is zero at 0 K, therefore, the resistance is also zero.

How fast do the electrons travel? A simple observation would tell an observer that the flow of electricity appears to be instantaneous when flipping on a light switch. Does that mean the electrons travel at the speed of light?

Drift Velocity When an electric field is applied to a conductor, it will set the electrons in motion in an overall direction opposite the applied field. While the electric field travels at nearly the speed of light, the overall speed of the electron from one end of the conductor to the other is quite slow and random in direction due to collisions. + - e

Determining the drift velocity in a wire. The total charge in a section of wire can be determined as follows: Where: n = number of carriers per unit volume A = cross-sectional area L = length of the conductor e = charge of an electron (the elementary charge)

Determining the drift velocity in a wire. Since all the electrons move along the conductor at the same average drift speed, the total amount of charge that moves through a cross section of wire is: Since v = d/t, we can find the time it takes for the total charge to move through any cross section by: Where vd = drift velocity and L = length of wire.

Determining the drift velocity in a wire. Substituting (1) into (2) for q, and (3) into (2) for q, and then solving for vd gives us: The number of charge carriers per unit volume (n) can be found as follows: Where: NA = Avogadro's Number M = the atomic mass number  = density

Example – Drift Velocity What is the drift velocity in the copper wires leading to a kitchen appliance that operates at 1 Ampere? Note: wire in your kitchen has to be capable of carrying 20 amps of current, therefore, it is specified to be 12 gauge. The cross-sectional area of 12 gauge wiring is 3.31 x 10-6 m2 Assume that 1 electron is donated by each atom. The density is 8.96 x 103 kg/m3. The atomic mass is 63.546 g/mole.

Finding the Drift Velocity in a Copper Wire First determine the number of charges per unit of volume (n) Now determine the drift velocity (vd) That’s only 0.08 m/hr!

Power Power = Rate at which work is done where: P = VI P = 1 Joule/second = 1 Watt P = VI = (1 Volt)•(1 Ampere) = 1 Watt V = W/q = 1 Joule/Coulomb I = q/t = 1 Coulomb/second Since V = IR and I = V/R: P = IRI = I2R P = V•V/R = V2/R

Example (Power) What is the power rating of a lightbulb in circuit where the current is 0.50 A and the voltage is 120V? P = VI P = 120 V•0.50 A P = 60 VA = 60 W

Power vs. Current and Power vs. Voltage (Ohmic Materials) What is the relationship between: power and current? Power and voltage? Current Power Voltage Power P = I2R P = V2/R

Energy Since power is the rate at which work is done the amount of energy required to complete a task is as follows: Total Energy = Power x time W = Pt

Example (Energy) How much energy is consumed by a lightbulb operating in circuit where the current is 0.50 A and the voltage is 120V for 1 hour? W = VIt W = 120 V•0.50 A•3600 s W = 216,000 J W = 216 kJ

Key Ideas A circuit is a closed path where current can flow. Current is the flow of charge. Resistance is the hindrance to the flow of charge. Ohm’s Law = voltage to current ratio (V/I) = Resistance. Resistivity is an intrinsic property of a material that is proportional the the resistance. An increase in length of a conductor will increase resistance. An increase in cross-sectional area of a conductor will decrease resistance. Power equals the rate at work is done and is represented electrically by P = IV.