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Study of Electric Charge and Electric Current




Static Electricity: Without going in to an in depth study of atomic theory, it can be said that materials are made of atoms. The simplest description of an atom is that it has a dense center called a nucleus that contains positively charged particles called protons and neutral particles called neutrons. Outside this nucleus is a region called an electron cloud which contains the low mass negative particles called electrons.

Most objects are electrically neutral. What this means is that the average number of positive and negative charges per atom are equal. Objects that exhibit charge are either positively charged or negatively charged. If an object is positively charged, there are fewer electrons than protons in the object. If an object is negatively charged, there are more electrons than protons in the in the object.

An imbalance of electric charge can be produced by rubbing two objects together. For example, if a glass rod is rubbed with a piece of silk, electrons will come off of the glass rod and attach themselves to the silk cloth. This will leave the glass rod with a small positive charge and the piece of silk cloth with a small negative charge. Also a rubber rod rubbed with a piece of fur will leave the rod negatively charged and the fur will be positively charged. The charging that occurs is the result of electrons being removed from one material while be attracted to the other. Such a transfer occurs because one material has a greater affinity (attraction) for electrons than the other material.

Note: Only the negatively charged particles, the electrons, can actually move.

Three terms for describing a substance's behavior where electric charge is involved.
Conductor: Materials, such as metals, allow electrons to move easily throughout.
Insulator: Materials through which electrons will not move.
Semiconductors: Materials, such as silicon and germanium, with a conductivity capacity between conductors and insulators.

About Electric Charge:
There are two kinds of electric charge, positive and negative.
Charges exert force on other charges over a distance.
Like charges repel, unlike charges attract

An Electroscope: A device for detecting electrical charge. Link to "Electroscope"

Charging by Conduction: In this process a charge is placed on a neutral object by touching a charged object to it.

Charging by Induction: In this process a charge is created on an object by bringing a charged object near to a neutral object, but we do not allow them to touch. If a negative charged object is brought near a neutral object it causes the electrons in the neutral object to move away to the other side of the object. This makes the side toward the negatively charged object to become positively charged. A similar phenomena will occur if a positively charged object is brought near a neutral object. The electrons in the neutral object move towards the positively charged object.

Observe the process of charging by induction: Link to "Charging by Induction"

Coulomb's Law: Charles Coulomb used a torsion balance (similar to what Cavendish used to measure gravity) to measure the force between two charged objects. His law tells us that the force between two charged objects varies directly with the magnitude of the charges and the varies inversely with the distance separating the two charges.

Equation: F = K q1 q2 / d^2; where F is force K is a proportionality constant q1 and q2 are the charges expressed in coulombs and d is the distance separating them. [ K = 9,0 x 10^9 N m^2 / C^2 ]

Charge is expressed in a unit called the Coulomb (C). One coulomb of charge is the the charge on 6.25 x 10^18 electrons. This means that the charge on one electron is 1.6 x10^-19 C

Determining the force between two charged objects:

A positive charge of 6.0 x 10^-6 C is placed 30 cm from a second positive charge of 3.0 x 10^-6 C. Calculate the force between the charges.

G: q1 = 6.0 x 10^-6 C; q2 = 3.0 x 10^-6 C; d = 30 cm
F: the electric force between the two charged objects
E: F = K q1 q2 / d^2
S: F = (9,0 x 10^9 N m^2 / C^2 * 6.0 x 10^-6 C * 3.0 x 10^-6 C) / (0.030 m)^2
A: F = +1.8 x 10^2 N

Neutral Objects do experience electrical force: Charged objects will either repel or attract other charged objects. It is also true that a charged object always attract a uncharged object. Neutral objects will experienced induction and an opposite charge to the charged object will form on the side nearest the charged object. This will cause it to be pulled towards the charged object.

Electric Fields: The area around an electric charge can be thought of as having numerous force vectors. Force vectors are seen as coming out from a positive charge and going in to a negative charge.

Electric Current: When electric charge flows it is called electricity or electric current.

Electric Potential: To move a charge from a position close to a second charge (A) to some distance away from the charge (B) work must be done. Its based on a force having to be applied to move the charge a specific distance. The work done is proportional to the magnitude of the charge moved. The difference in electrical potential between the two points A and B respectively, is a measurement of the work done per unit charge. The unit is called the volt and the measurement is defined as 1 volt is 1 J/C (One joule per Coulomb). Electric Potential or Voltage is measured using a device called a volt meter.

Electric current is the flow of electrons from a high potential to a lower potential.

Electric Current: Electric current is measured in Amperes or Amps (A). An Amp is defined as the flow of one coulomb of charge per second. Electric Current is measured using a device called an ammeter.

Electric Power: Electrical Power is expressed in watts as is mechanical power. Electrical power is found by multiplying the voltage in a circuit (electrical path) by the current flowing through the circuit. In turn this power can be expressed in terms of W / t, such that it is possible to calculate hoe much energy is involved in the flow of current through a circuit.

A six volt battery delivers 0.5 A of current to an electric motor connected across its terminals.

First, what is the power rating of the motor

G: I = 0.5 A; V = 6 V
F: Power
E: P = V I
S: P = 6 v * 0.5 A
A: P = 3 W

Second; what is the amount of energy used by the motor in 5 minutes.

G: P = 3 W; t = 300 s
F: Energy by calculating work
E: W = P t
S: W = 3 W * 300 s
A: W = 900 J

Electrical Resistance: Even materials which are called conductors cause some degree of resistance to the flow of electrical current through the conductor. This resistance causes a potential difference such as at the two ends of a wire through which a current is flowing.

George Ohm found a relationship between this potential difference and the current flowing through the object. This relationship is known as Ohm's law and is written as:

I = V / R; where I is current; V is voltage and R is the resistance.

Resistance is measured in a unit called ohms, symbolized by the Greek letter Omega (W). 1 ohm is the resistance that allows 1 A of current to flow through a potential difference of 1 V.

Determine the current that flows through a 30 ohm resistor that has a potential difference (voltage) of 120 v.

G: V = 120 v; R = 30 ohms (W)
F: Electric Current (I)
E: I = V / R
S: I = 120 v / 30 W
A: I = 4 A

Electric Circuit Symbols: Most textbooks about physics and electricity contain at least a basic list of electric or electronic symbols for drawing schematics for electrical circuits. The most basic symbols used represent a conductor, switch, fuse, capacitor, fixed resistor, variable resistor (rheostat), ground, electric connection, no electric connection, battery, lamp; dc generator, voltmeter and ammeter.

Electric Schematic: A drawing of a simple circuit.
 
 

How is current controlled in a circuit? Current (I) can be controlled by changing V and/or R. The voltage source can be fixed or variable. The Resistance can be fixed or variable. Also, what the electrical energy is converted to depend on the device through which the current flows. A motor converts the electrical energy into mechanical energy. An electric lamp converts the electrical energy into light energy. Whenever electric energy is transformed into another form of energy some always ends up as heat energy. Some devices are designed to maximize this conversion of electrical energy to heat, such as in the example of a toaster or a curling iron.

Heating effect of Electric currents: (Electric) Power is defined as the math product of voltage and current. (P = V I) Using Ohm's law to substitute for voltage the Equation will become P = I R * I or I^2 R.
The relationship between heat energy and electrical energy is defined by the equation Q = I^2 R t. Consider this example:

A heater has a resistance of 10 W. It is operating on 120 v.

What is the current through the resistor?

G: V = 120 v; R = 10 W.
F: Electrical Current (I)
E: I = V / R
S: I = 120 v / 10 W.
A: I = 12 A

What is the amount of thermal energy supplied by the heater during a 10 s time interval?

G: R = 10 W; I = 12 A; t = 10 s
F: The amount of heat energy (J)
E: Q = I^2 R t
S: Q = (12 A)^2 * 10 W * 10 s
A: Q = 14,400 J or 14.4 kJ

Transmission of Electrical Energy: Historically the first locations for Electrical generating plants were along rivers where dams could and would be built. The gravitational energy allowed water falling downwards to drive turbines that spun the electrical generators that made the electricity. Often the electrical generating plant was not anywhere near to the places where the electricity was needed. The problem faced as the role played by electricity increased was one of long distance transmission. Thomas Edison, a well known inventor of such things as the light bulb wanted to go with DC electricity. However, because of the effect of electrical resistance on wires, especially wires of significant length DC current was not efficient as the large wires having a resistance of ~0.2 ohms carried the current.

For example, suppose there was a home 3.5 miles from the generating plant, connected by these large wires. The resistance in the wires is 3.5 km x 2 (think in terms of the round trip) x 0.2 ohms. This equals a total resistance of 1.4 ohms for the 7 km path. Next take an electric stove that uses 41 amps of current to operate. The power lost (wasted) in the wires is P = I^2 R, which translates into (41 amps)^2 * 1.4 ohms. This yields 2400 watts of power lost, just by using that single stove.

Nicola Tesla pushed for AC current to be generated and transmitted long distance. Unlike DC current where the electrons actually have to make the long trip out to the household appliance and back to the generating station, AC current involves the electrons changing directions 60 times a second (In Europe 50 times a second), thus never having to travel long distances and waste so much of the electrical energy. Tesla is considered to be among the great scientists and inventors of the late 19th early 20th century. He definitely was a rival of Thomas Edison.

The measure of electrical energy: Because the joule is a very small amount of energy, the electrical companies measure the electricity you use in a much larger quantity called the kilowatt-hour (kWh). A kilowatt hour is the energy represented by 1000 watts delivered continuously for 3600 seconds (which is one hour). Math wise this is 1 kWh = 1000 J/s (or 1000 W) * 3600 s = 3.6 * 10^6 J of energy.

An example of the the cost of operating an electrical appliance:

A color television set draws 2 A when operated on a 120 v system.

How much power does it use?

G: I = 2 A; V = 120 v
F: Power used
E: P = V I
S: P = 120 v * 2 A
A: P = 240 W

If the TV is operated for 7 h per day for a 30 d month, how much energy will it consume?

G: P = 240 W; t = 7 h/d * 30 d
F: Energy (Rem: Energy = Work so solve for work)
E: W = P t
S: W = 240 W * 210 h
A: W = 50,400 W h = 50.4  kWh

If the of operating is set at $0.08 per kWh, what is the cost of operating this TV?

G: W (the energy equivalent) = 50.4 kWh; Cost = $0.08 per kWh
F: Total cost to operate the TV
E: Total Cost = W * Cost / kWh
S: Total Cost = 50.4 kWh * $0.08 / kWh
A: Total Cost = $4.032