Unit 11 Electric Potential and Current

Our knowledge of static electricity will assist us in learning about electrical current. Though humankind have known about electrostatics for centuries, electrical current has only been observed and studied for the last two centuries. Electric current is the useful form of electricity that allows us to use our appliances.

We know that electrical charges are surrounded by fields that exert forces on other charges. In order to generate current, there must be a force acting on the charges that flow through a conductor. The simplest way to visualize electrical current would be if we brought a positive test charge close to another positive charge and released it. The electric field would push the charge away, resulting in current. We can see that work must be done in order to bring the test charge closer to the positive charge. This means that when the test charge is brought close to the positive charge, it must have a form of electrical potential energy. Once the charge has energy, it is capable of doing work such as illuminating a lightbulb, turning a motor or producing heat.

Electric Potential

We know that a positive test charge, q, an infinite distance away from some positive charge Q, will experience no force and have no potential energy. In order to move q towards Q, we must exert a force over a distance and do work. As we approach Q, the amount of force required to push the test charge must increase. The closer to Q we get, the more work we must do and the more potential energy the test charge acquires. If we repeated this task but with a test charge of 2q, we would have to push it with twice the amount of force. Therefore we would end up doing twice the amount of work and the test charge would end up with twice the amount of potential energy. Increasing the charge on q to 5q would result in 5 times the work and 5 times the acquired potential energy.

In each case, if we took the ratio of the acquired potential energy to the charge of the test charge, we would find that whether the charge was q, 2q or 5q, the ratio of potential energy to charge would be the same. This ratio is referred to as the electric potential.

V = Work / Charge = Energy / Charge

Units for electric potential are Joules / Coulomb. We define 1 J/C as 1 volt. Electric potential or voltage is a measure of the energy per charge. We know that nature prefers to go from states of higher energy to lower energy so we would expect that when given the opportunity, the charge with high electric potential would flow towards a place where it would have a lower electric potential. Along the way, it would release the energy by doing work or producing heat.

Producing Electric Potential

In order for charge to flow as electrical current, there must be a difference in potential. Charge will spontaneously flow from high to low potential, just as water will spontaneously flow downhill. There are several ways of giving charge potential. The following is a partial list of ways to induce potential:

1) Electrochemical Cells - a chemical reaction is used to give electrons a high potential. An example would be a zinc and copper metal immersed in an electrolyte, like sulfuric acid. Both metals are capable of losing electrons when they react. However zinc has a greater ability to lose electrons than does copper. Consequently the zinc will lose 2 electrons and be released into the electrolyte as a Zn^+2 ion, leaving behind two electrons. As the negative charge builds up on the zinc electrode, it gains electric potential. If a pathway to the copper electrode is provided, the electrons will flow to the copper, where the potential is lower. This would stop quickly if the electrons were allowed to collect on the copper electrode. However, the electrons are pulled off of the copper by the H^+1 (actually H3O+1) ions in the electrolyte. The reaction at the cathode (in this case, the copper electrode) is 2 H+1 + 2 e --> H2. This reaction prevents excess electrons from building up, keeping the potential of the cathode lower than the anode (in this case, the zinc electrode).

2) Photoelectricity - energy from photons of electromagnetic radiation are absorbed by electrons giving them energy and electric potential

3) Electromagnetic Induction - a changing magnetic field induces a potential across a conductor. This will be discussed in much more detail in the Electromagnetic Induction unit.

4) Piezoelectricity - a crystal is bent slightly and induces an electric potential.

Uses of Electric Potential

We need a difference in electric potential to produce a current. This current carrys charge with potential energy that is capable of doing work. The work that can be done involves:

1) Producing heat- As electrons move through the conductor, they collide with the atoms in the conductor, losing some of their energy to the atoms. Once the atoms gain energy, the vibration of the atoms increases, showing up as an increase in temperature. This easily seen on an electric stove.

2) Producing motion - As the electrons move through a conductor, they set up a magnetic field around the conductor. If there is a magnet in the immediate vicinity, it will experience a force due to the induced magnetic field. This is the principle behind an electric motor. We will discuss this in much more detail in the unit on Magnetism and Electromagnetism.

3) Producing light - Electricity can produce light in 3 different ways.

A) in an incandescent lightbulb, the flow of charge creates a large enough increase in the vibration of the atoms and their electrons in the filament to cause the electrons to emit energy in the visible range of the electromagnetic spectrum.
B) in a fluorescent light, the flowing electrons collide with the electrons in the fluorescent paint inside of the light. Some energy is transferred to the paint electrons which then re-emit the energy as light.
C) in a gas light ("Neon light"), the flowing electrons collide with the electrons in the gas inside of the lamp. Some energy is transferred to the electrons in the gas which then re-emit the energy as light. Different gases produce different colors because of their unique electron arrangements.

Calculating Electric Potential

Electric potential (V) can be calculated by using the following formulas. The first equation relates the Electric potential to the field strength and the distance from the charge.

V = E*d

V = Electric potential or voltage (volts or J/C)

E = Electric Field Intensity (N/C)

d = distance from charge (m)

If we break the field intensity down into more basic units, the electric potential can be calculated using the following:

V = kQ/d

V = Electric potential or voltage (volts or J/C)

k = 9.0 x 10⁹ Nm²/C²

Q = charge (C)

d = distance from charge (m)

Electric Current

The rate of flow of charge is probably easier to measure than the amount of charge that passes through a conductor. We define the rate of flow of charge as the electric current. The equation that relates current, charge and time is:

I = Q/t

I = electric current (Coulombs/sec or Amperes) Q = charge (C) t = time (sec)

If we know the potential and current in a circuit and the amount of time that the current flows, we can determine the quantity of charge, the energy consumed.and the power or rate of energy consumption.

Electric potential or voltage is energy per charge and current is charge per time flowing through a circuit. If we multiply the voltage by the charge we can determine the amount of energy consumed.

Energy = V*Q = J | C = J
C |

Since Q = I*t,

Energy = V*I*t

Power = Energy / time = V*I

The electric company bills you for kilowatt*hours, a unit of energy, not power.

Requirements For Electric Current

In order for there to be current flowing through a conductor, there must be:

1) a conductor for the charge to flow through. Electrons flow through metals, positive and negative ions can flow through solutions containing electrolytes.

2) a potential difference between the two ends of a conductor. Charge will flow from high to low potential.

3) a complete path between the two different potentials. In most cases, electricity flows in circuits. These circuits must be complete, with no interruptions.

Measuring Potential and Current

We use an ammeter to measure electric current. The ammeter is placed in the circuit in such a way to measure all of the current passing through the circuit at that point. The ammeter is connected in series with a circuit element so to allow only one path for the electrons to flow. The ammeter offers very little resistance so that it has minimal effect on the amount of current flowing through the circuit.

We use a voltmeter to measure potential. For example, we may want to measure the potential difference between the positive and negative terminal of a power source. This tells us the difference in potential between the two terminals. We also may measure the potential across a load (in parallel with the load) in the circuit to measure the drop in potential as the current flows through the load.

Alternating Current Vs Direct Current

A battery provides a steady potential so that the current it produces is steady. This type of electricity is referred to as direct current (DC).

The electricity that an electrical outlet provides is alternating current (AC). The origin of the electricity provided to your house is an electromagnetic generator driven by steam or hydro power. In alternating current, the current changes direction at a rate of 60 Hz (50 Hz in Europe). This means that the lights are actually flickering at a rate of 120 Hz.

Capacitors

A capacitor is a circuit element that can store electrical charge and release it in a "burst". The capacitor consists of two conductors in close proximity separated by an insulator. When the capacitor is connected to a battery, one side of the conductor becomes negative and the other side becomes positive. The capacitor is now charged and will remain that way until it is connected to a complete circuit. When it is connected to a complete circuit, the capacitor will discharge creating a momentary burst of current.

A capacitor is capable of handling a certain charge to voltage ratio. This ratio is referred to as the capacitance.

C = Q/V

C = Capacitance (Farads) Q = Charge (Coulombs) V = Electric Potential (Volts)

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