Electrical Energy & Current

Introduction to Electric PE, Electric Potential, and Potential Difference Intro to Electric Potential

Electrical Potential Energy PE associated with a charge due to its position in an electric field. Analogous to PE g PE g of an object results from its position in a gravitational field (mgh) Is a component of mechanical energy ME = KE + PE grav + PE elastic + PE electric

Electric PE in a Uniform Electric Field A uniform field is one that has the same direction at all points, such as between two parallel plates Remember: electric field lines are always directed from away from positive and toward negative

Electric Potential Energy Recall that Δ PE = -W When charge q is released at point a, electric force will move the charge to b, i.e. The electric field does work on the charge q W = Fd Since F = qE (E = F/q) W = qEd PE b -PE a = -qEd Δ PE = -qEd

PE as a charge moves in a uniform electric field Movement of charge+ charge- charge Along ELoses PE (where + “wants” to go) Gains PE Opposite EGains PELoses PE (where – “wants” to go)

Similarity of PE electric and PE g PE g = mgh m is mass g is gravitational field h is distance above a reference point PE elect = -qEd q is charge E is electric field strength d is distance from reference point The (-) sign indicates the PE elect will increase for –q and decrease for +q Using dimensional analysis, what is the unit of PE elect ?

Potential Difference Electric potential is the ratio of PE elect to charge q Represents the work needed to move a charge against electric forces from a reference point to some other point in an electric field The unit of electric potential is what?

Potential difference The change in electric potential The difference in electrical potential between two points Is the work that must be done against electric forces to move a charge from one point to another divided by the charge

Potential Difference Unit is the volt (V)

Potential Difference in a Uniform Electric Field Varies in a uniform field with displacement from a reference point Where d is displacement parallel to the field Use this equation to determine potential difference between two points in a field

Potential Difference at a Point Near a Charge One point is near the charge The other point is at infinity Use this equation to find the potential difference at a single point

Electric potential due to multiple charges Electric potentials are scalar quantities (whew!) So…. Total potential at some point in a field is the simple sum of the potentials due to each charge Keep track of signs!

Sample Problem As a charge moves x a = 4.0 cm to x b = 8.0 cm in a uniform field of 350 N/C, it loses 4.5 x J of potential energy. What is the magnitude of the charge? What is the potential difference between the two points a and b?

17.2 Capacitance Capacitors are devices that store electrical PE Often constructed of parallel metal plates When connected to a battery, the plates become charged When fully charged, ∆V cap = ∆V bat

Capacitance Ability of a conductor to store energy in the form of separated charges Unit of capacitance is the farad, F

Capacitance of a Parallel Plate Capacitor in a Vacuum A is the area of the plates E 0 is permittivity constant for a vacuum = 8.85 x C2/Nm2

Dielectric Materials Insulating material placed between the plates of a capacitor Increases the ability of a capacitor to carry a charge

Discharging a Capacitor Capacitors are devices that store charge When discharge, they release charge Computer keyboards are an example of capacitors in action

Capacitance of a Sphere R is radius Because the earth has a large radius, it has a very large capacitance i.e., the earth can accept or supply a very large amount of charge without changing its electrical potential This is why the earth is “ground,” (reference point for measuring potential differences)

Energy and Capacitors PE Stored in a Charged Capacitor

Current and Resistance Current is the rate of movement of charge Rate of movement of electrons through a cross-sectional area

Sample Problem If current flowing through a light bulb is A, how long does it take for 1.67 C of charge to pass through the filament of the bulb? 2.00 seconds

Conventional Direction of Current Depending upon the circumstances, either positive, negative, or both can move. Particles that move are called charge carriers By convention, direction of current is defined as the direction a positive charge moves or would move if it could. In metals, only electrons can move. Good conductors permit charge carriers to move easily Electrons in metals Ions in solution (electrolytes)

Conventional Direction of Current

Drift Velocity Recall the structure of metals Valence electrons move about randomly due to their thermal energy Their net movement is zero But if an electric field is established in the wire, there is a net movement of electrons against the electric field (toward +) Drift velocity animation

Drift Velocity It is the electric field that exerts force and thereby sets charge carriers in motion E propagates very rapidly (near speed of light) Charge carriers move more slowly, in an erratic path, Called drift velocity Slow: e.g. in a copper wire carrying a 10.0 A current, v drift = 2.46 x m/s Consider motion of an electron through a wire

Resistance to Current Opposition to electric current Unit of electrical resistance is the ohm ( Ω ) More commonly known as Ohm’s law

Ohmic and Non-ohmic Materials Materials which follow ohm’s law are ohmic materials Resistance is constant over a wide range of potential differences (linear) Non-ohmic materials have variable resistance (non- linear Diodes are constructed of non-ohmic materials

Other Factors Affecting Resistance

17.4 Electric Power A potential difference (∆V) is necessary to cause current (I) Batteries supply chemical energy (PE chem ) which can be converted into electical PE Generators convert mechanical energy into electrical PE E.g. hydroelectric power plants Coal or natural gas powr plants Nuclear power plants

Direct and Alternating Current DC current flows in one direction only Electrons move toward the (+) terminal Conventional current directed from (+) to (-) AC current Terminals of source of ∆V constantly switch Causing constant reversal of current, e.g. 60 Hz Rapid switching causes e - s to vibrate rather than have a net motion.

DC and AC DC constant uni-directional AC not constant bi-directional

Energy Transfer In a DC circuit Electrons leave the battery with high PE Lose PE as flow through the circuit Regain PE when returned to battery (battery supplies PE through electrochemical reactions)

Electric Power The rate of conversion of electrical energy SI unit is the watt (W)

Other Formulas for Power

Kilowatt-hours How utility companies measure energy consumed Is the energy delivered in one hour a constant rate of one kW 1kWh=3.6 x 10 6 J What is the cost to light a 100 W light bulb for 1 full day if the electric utility rate is $ per kWh?

Transmission Lines Transit at high voltage and low current to minimize energy lost during transmission Compare the equations…. P = I 2 R P = I∆V