Electricity

Electrostatics

What is the reason for the warnings printed on gas pumps cautioning us not to get in and out of the car when we’re pumping gas? The reason is that cars pick up electrostatic charges as they run, and the car’s tires insulate that charge from the ground. Electrostatics is the study of electrical charges on objects at rest.

There are two fundamental charges: positive and negative. We know that similarly charged objects repel and oppositely charged objects attract. Besides this, objects that are neutral (i.e. objects with an equal amount of positive and negative charge) are attracted to both positive and negative objects. Why do we know this? Let’s first review the basic model of the atom.

The very center of the atom is a tiny concentrated region that contains positive particles (protons) and neutral particles (neutrons), called the nucleus. The number of protons in the nucleus uniquely determines what element it is. This number will not change unless a “drastic” nuclear event occurs (i.e. fission or fusion). In the large region of space around the tiny nucleus there is likelihood that you will find negative particles (electrons). In neutral atoms, the number of electrons equals the number of protons. In order for an object to gain a negative electric charge, it gains extra electrons. To pick up a positive charge, the object loses electrons. Thus, electrons are the “mobile fluid” responsible for charging objects. An object will always have the same amount of protons before and after gaining an electrostatic charge.

Some elements are naturally good conductors of electricity. Conductors are materials in which electrons flow easily from atom to atom. Metals are excellent examples of conductors. Dielectrics, or insulators, are materials in which the electrons are tightly bound to a particular nucleus. Rubber, plastic, and air are examples of good insulators. Under conditions with very high voltages, even insulators may have electrons travel throughout the material.

Why are neutral conductors and neutral insulators attracted to charged objects? The explanation is a little different for each. When a negatively charged object is brought near a conductor, the electrons in the conductor are repelled by the electrons in the charged object. The free electrons in the rod are forced to move to the opposite side of the rod, leaving the positive nuclei to attract the negative object. This process is called electric induction and is represented in the following diagram:

Electric Fields

In the vicinity of charged objects, there exists an electric field in which other charged objects will experience forces. The charged objects have “lines of force” or “flux lines” emanating from them. The direction of the force exerted on a positive test charge placed near a charged object is shown by placing arrowheads pointing into the object to represent a negatively charged body, or arrowheads pointing out of the object if it is a positively charged body. For example, the first diagram below shows that a positive test charge is repelled from a positive central charge (+Q). The second diagram shows that the same positive test charge is attracted to a negative central charge (-Q).

• Electric field lines always begin at and point away from positive charges. They point toward and end at negative charges.
• The number of field lines entering or leaving a charge is representative of the magnitude of each charge.
• Field lines never cross.
• The electric field is stronger in regions where the field lines are closer together and weaker in regions where the lines are far apart.
• Electric field lines are perpendicular to the surface of the charged, conducting object
• Electric field lines do not exist within a charged, conducting object.

For example, what would the electric field pattern look like if two protons (+2e) were in the vicinity an electron (-e)? The following diagram will show the pattern:

What do field lines look like in the vicinity of two repelling charges? For example, the following diagram shows the electric field pattern in the vicinity of a +6 Coulomb charge and a +4-Coulomb charge:

Electromotive Force

Previously we covered that work is done when forces displace objects. When this occurs energy is transferred from one storage mode into another. In this lesson, we will study how energy is transferred in electrical circuits caused by electromotive force.

Electrical circuits may be powered by a variety of energy sources. Here are a few examples of devices that serve as energy sources for circuits:

• Batteries: Devices that transfer chemical energy to electrical energy.
• Generators: Devices that transfer mechanical energy to electrical energy.
• Solar panels: Devices that transfer radiant energy to electrical energy.

Each of these devices applies an electromotive force (EMF) that does the work on the electrons in the circuit to transfer energy.

The wires in a circuit provide a pathway for energy transfer. For example, using a simple circuit between a battery and a light bulb, the electrons within the circuit carry energy from the battery to the bulb. These electrons are never created nor destroyed during the process of transferring the chemical energy in the battery to radiant energy shining from the bulb. In a circuit powering an electric blanket, for example, electrical energy is transferred to heat energy.

The electromotive force (EMF) is the potential energy per unit charge that can be transferred to the electrons in a circuit. The units are “joules per coulomb,” which is defined to be a volt. The EMF is measured by finding voltage, or electric potential difference, across the two ends of the power supply when there are no electrons flowing. If current is running through the power supply, the voltage measurement is actually less than the EMF. Thus, the EMF is the maximum possible potential difference measured across a power source.

Electric Current

Previously you have seen that an electromotive force is responsible for providing the potential to move electrons in a circuit. You also learned that electrons are charged particles that carry energy in a circuit. In this lesson, we will formally define the concept of electric current.

When there is a difference of pressure across the two sides of a water pipe, water will flow from a region of higher pressure to a region of lower pressure. Thus, water current is established in the pipe, and this current is measured in gallons per second. Likewise, when there is a difference of electric potential (voltage) across a wire, electrical current is established. Electric current (I) is a measure of the number of electrons (measured in Coulombs Q) that pass a point in a circuit over a certain amount of time (t). The equation is written like this:

I = Q / t

The units of electrical current are Coulombs per second which is defined as the Ampere (A).

Electrical current may be classified as “direct” or “alternating.” Direct current (DC) occurs when the electrons circulate in one direction throughout the circuit. Batteries naturally produce DC current. The electrons move quickly in a DC circuit, but the energy they carry is transmitted almost instantaneously throughout the circuit. Alternating current (AC) occurs when the electrons vibrate back and forth at a particular frequency. Generators naturally produce AC current. As we shall see in a later lesson, AC current is typically used when a significant amount of energy is transferred through long distances.

Resistance and Ohm’s Law

When electrons move in an electric circuit the parts of the circuit resist the movement of the electrons. This property in an electric circuit is called resistance. Some electrical devices allow electrical current to flow easily through them. We say that these devices have a low resistance to the flow of electrons. Devices with a high resistance, on the other hand, resist the flow of current. These devices require a power source with a larger voltage to establish the same current as a low resistance device. Consider a simple circuit consisting of a battery and some device (like a light bulb). As the voltage of the battery increases, the current running through the circuit will increase. The resistance of a device is the ratio of the voltage across it to the current running through it as demonstrated on the following graph:

y = mx + b

V = R I + 0

V = I R

where V = voltage, I = current, and R = resistance.

The measurement unit of resistance is the ohm ( Ω ) and is defined as the ratio of volts to amps.

DC Circuits

One way to increase the electrical resistance is to put a string of devices in series along the same electrical path. The total resistance of the path is the sum of all the individual resistances in the path as follows:

Circuits can also be wired in parallel where there are multiple paths for the electrons to take. With the extra pathways, the resistance of the circuit drops as follows:

Most electrical devices are a combination of series and parallel devices. For example, consider the following combination circuit:

Thus, applying Ohm’s law, the total current drawn by the circuit is:

I = V / R total = (12V) / 12 Ω ) = 1 A

Question

The circuit shown below has a total resistance of 24 Ω. What is the total current drawn by the battery?

1. 0.25 A
2. 4.0 A
3. 5.0 A
4. 144 A

Reveal Answer

The correct answer is A. Applying Ohm’s Law to the circuit, we obtain the current by dividing the voltage of the power supply by the total resistance:

I=V/R total = (6.0V)/(24 W ) = 0.25 A

To calculate the total resistance, first determine the resistance of the 4 W and 12 W resistors in parallel. This is 3 W as shown earlier in this lesson. Now the circuit looks like the following series circuit:

The total resistance is the sum of all three resistors:

R total = 9 + 3 + 12 = 24 W

AC & DC Circuits

Previously we covered that electrical energy is delivered via direct current (DC) or alternating current (AC). In this lesson, we will study the applications that are appropriate for DC and AC.

When current flows through a wire, the wire will heat up because of the wire’s resistance. For applications that require low current flow through short distances, the amount of heating in the wires is negligible. Batteries produce DC and are used to deliver energy through short distances in circuits.

When distributing large amounts of energy to electrical power grids, high currents are needed for energy transmitted at common household voltages (120V). The amount of line heating in the wires is prohibitive with these large currents, costing millions of dollars per mile of wire every hour just to power a medium-sized city. When AC is used, however, step-up transformers increase the transmitting voltage and drop the current to levels where the energy loss due to line heating is acceptable. At the household level, step-down transformers drop the voltages back down to 120V and raise the current to levels demanded by the consumer. Transformers only operate with AC current.