Conductors, Capacitors, Dielectrics

Explanation of Conductors

The electric wire must have the proper number of conductors

Older two-wire electrical circuits, such as the two circuits depicted at the right of our sketch may provide only the hot and neutral wires and no ground wire. 

The electrical circuit wire must be properly routed and secured between the electrical panel and the receptacle location, and must be properly secured at the junction box that is to hold the electrical receptacle. 

Main Concepts of Electric Forces and Fields

Electric forces and electric fields are vectors, electric potentials are scalars

Electric fields point in the direction of the force on a positive test charge

Capacitance is the ratio of charge to the potential for a given conductor the plate seperation and the permittivity or dielectric constant of a system of parallel plates depends only on the physical characteristics of the capacitor (i.e. Surface area, plate seperation, dielectric material)

Dielectric Explanation

A dielectric capacitor consists of two metal sheets placed on either side of a layer of dielectric material.

Dielectrics are materials like glass or plastics (polymers) which are insulators. The behavior of a dielectric is determined by its dielectric constant value. 

Important Vocabulary

Electrostatics – is the study of interaction between electric charges which are not moving

Conductors – are materials in which the electrons are free to move. Some examples such as silver, copper, gold, and mercury as metals

Electric Fields – exist in the space surrounding a charged particle or object

Capacitor- stores electric charge and consists of two conductors seperated by an insulator known as a dielectric

Dielectric – is an electrical insulator that can be magnitize both electric charges by an applied electrical field

Electric Current – is the rate of flow of electric charge. Used in Amperes (I) where 1 Ampere is 1 coulumb/second

Electrical Resistance refers to the opposition offered by a substance to the flow of electrical current. Unit of resistance is Ohm

Capacitor Explanation

A capacitor which is an energy-storage device is used to store energy between two conductors. These conductors are also called plates. An insulator is placed between these two plates.

These plates are charged in order to store energy. One of the main function of a capacitor is to work as a filter. In this process blocks DC (Direct Current) and passes AC (Alternating Current). 

Important Formulas

Electric Charge: q = n e ; where e = 1.6 X 10-

19 C; (q) is the total charge on an object, (e) is the fundmental unit of charge, (n) is the number of total charges

Coulomb’s Law: F = k Q1 Q2/r2 ; where k = 9 X 109 N m2 /C2 ; (F) is the two charges exerted a force (Q) is the magnitude of the charge while (r) is the squared distance of charge

Important Formulas # 2

Electric Field: E = F/q or F = q E ; (E) is the magnitude of electric field, (F) force exerted om test charges, (q) is the magnittude of the charge of test particle

Electric Field to a Point Charge: E = k Q /r2 ; (E) is the magnitude of electric field, (F) force exerted om test charges, and (r) is the distance from the charge

Important Formulas # 3

Electric Potential: V = PEa / q ; (PEa) is the potential energy, (q) per unit charge (V) is the electric potential at point

Capacitance: C = Q/V ; (C) is the ratio of the charge stored, (Q) is the potential difference, (V) is between the conducting surfaces

Electric Current: I = Q/t ; (I) is the electric current in Amperes

Electrical Resistance: R = p L/A ; (R) is the resistance of metal wire, (L) length, (A) cross-sectional area, (p) is the resistivity

Ohm’s Law: I = V/R or V = IR ; (I) stands for electric current and (V) stands for voltage of current and (R) stands for the resistivity

Electric Circuits

Main Concepts

An electrical network with a closed pathMeasured in terms of number of charge

carriers orParticles containing an unit electric chargeThe current flows through a resistance

Circuits

Series Circuit - is an electric field with only a single path for electric current to travel. The current through each circuit is the same.

Parallel Circuit - is an electric circuit with more than one path fore electric current to travel. The current is divided among the branches of the circuit. The voltage drop is the same across each branch.

Kirchhoff’s Rules

Used in junction with Ohm’s law in solving problems involving complex circuits

All junctions in a circuit have the same potential

The sum of all the potentials around a closed loop is zero

The sum of all the currents around a closed loop is zero

The sum of the charges stored at all junctions in a closed loop of a circuit is zero

RC Circuits/Kirchhoff’s Rules # 2

RC Circuit - consists of a resistor and a capacitor connected in series to a DC Power source.

First Rule or Junction rule The sum of all currents entering any junction point

equals the sum of all currents leaving the junction point.

Based on the law of conservation of electric chargeSecond Rule or Loop Rule

The algebraic sum of all the gains and losses of potential around any closed path must equal zero.

Based on the law of conservation of energy

Suggestion for Using

Assign a direction to the current in each individual branch of the circuit- Positive on each side of resistor where current enters, negative sign on the side where current exits

TIPS TO HELP YOU OUT

Things to Think About

DC Circuits

Draw an illustration correctly labeling everything before beginning

Check to make sure you have assigned the proper signs to potential differences when using Kirchhoff’s rules

With Kirchhoff’s rules, you guess the directions of the currents (if correct, positive; incorrect, negative)

Capacitors in DC Circuits are circuit disrupters, meaning no current across the plane

Ammeters are connected in series with the resistance and voltmeters are connected parallel to them

Electric Currents

Make sure not to confuse resistance with resistivity

Make sure to calculate cross-sectional area and correctly convert cm squared to m squared

Remember how to calculate the power dissipated in a resistor

Capacitance

Electrical potential is a property of spacePotential energy: a property assigned to a

chargePotential difference & difference in potential

energy is not the samePotential is zero at great distance from a

charge

Electric Fields

For our purposes, an object cannot be affected by its own field

The direction of electric field is the direction of the force the field exerts on a positive charge or the direction of electric field is the same as the direction from high potential to low potential

For the motion of a charged particle in an electric field, use the system of equations for constant acceleration that we use for projectiles

Practice Problems

Electric Currents

A) Determine the electrical resistance of a 20.0 m length of tungsten wire of radius of 0.200 mm

B) If the temperature of the wire does not change, determine the resistance of the same wire if it is stretched to a length of 60.0 m.

The resistivity of tungsten is 5.60 x 10-3 (symbol) m.

Electric Currents Contin.

An electric immersion heated rated at 250 watts is inserted in a 100 gram aluminum cup which contains 200 grams of water.

Initial temp of cup and water: 20.0 degrees C

Determine the time required for the temperature of the cup and water to rise to 90.o degrees C.

**The specific heat of aluminum is 0.220 cal/g C and water is 1.00 cal/g C

DC Circuits

A 5.00 ma current causes a galvanometer of internal resistance 10.0 ohms to deflect full scale.

Determine the resistance that must be added in order to convert the galvanometer into

- a) a voltmeter which measures potential differences from 0-50.0 volts

- b) an ammeter which measures currents from 0-1.00A