Electric Current

• The flow of electric charge from one place to another is called an electric current.

  • current = charge moved / time interval

• In order to get a charge to flow there has to be:

  • a force which implies an electric field or,

  • a potential energy difference which implies a potential difference

• The direction of the current is the flow of the positive charges

  • even though most currents are the flow of the electrons which are negative – historical accident.

  • current sounds like it should be a vector but it is not.

• The SI unit of current is the ampere and the symbol is A.

• For a given current through a material with known properties, we can find the speed of the charges.

  • This speed is called the drift velocity.

• For a 1 A current in a copper wire with a diameter of 2 mm we find the drift velocity is ~10^-5 m/s.

  • it would take an electron hours to travel 1 meter along the wire.

• The electrons in a material are not actually stationary, at room temperature they have speeds which are ~1000 km/s.

• The speed of electrons due to their thermal motion is still slower than the speed of electricity along a wire.

  • the speed of electricity down a wire is ~150,000 – 300,000 km/s

• The speed of electricity is the speed of the electric field.

Voltage Sources

• A current flows from one place to another as long as there is a potential difference between those two places.

• The other name for a potential is voltage.

• There are many ways a creating the potential difference:

  • charged capacitors,

  • batteries (fuel cells),

  • Van der Graaff generators,

  • generators (dynamos and alternators)

• Voltage sources are not sources of charge (they don’t store electrons), voltage sources are sources of energy

Batteries

• Some chemical reactions involve the transfer of electrons from one atom to another. For example:

  • if you insert a zinc rod into a solution of copper sulfate, the zinc rod will dissolve into the solution and copper metal will plate the rod.

  • the solution contains Cu2+ ions which are missing two electrons: the zinc atoms in the rod are neutral.

  • in the reaction, two electrons are moved from the zinc to the copper.

  • now charged, the zinc dissolves in the solution and the neutral copper coats the rod.

• A battery generates a voltage drop across its terminals by tapping into the electron flow in such chemical reactions.

  • another name for a battery is an electrochemical cell.

• To prevent plating we use two half cells and connect them with a salt bridge. The two metals are often called electrodes.

• Modern batteries and fuel cells are still based on the principle of tapping into the electron flow in chemical reactions.

EXAMPLE 1:

Is electric current stored in a battery?

• No. Voltage (potential energy), not current, is stored in batteries. The voltage will produce a current in a connecting circuit. The battery moves electrons already in the wire.

Resistance

• Given a potential difference (voltage drop), the amount of current depends upon the resistance between the two points.

• The higher the resistance, the smaller the current for a given voltage drop.

• The resistance is defined to be

  • resistance= voltage drop / current

• The unit of resistance is the ohm

  • the inverse of resistance is conductance which is measured in Siemens.

• The resistance is a constant for many materials as a function of the current and voltage.

  • if it’s not the resistance is sometimes called static resistance.

• Such materials are called Ohmic.

• For such materials, the previous equation is rearranged to give

  • voltage drop=current×resistance

  • which is known as Ohm’s Law

• The three factors which influence the resistance are:

  • the physical dimensions of the material

  • the material the current flows through,

  • the temperature.

• The resistance:

  • increases with the length of the material the current flows through

  • decreases with the cross sectional area.

• For resistors with the same physical dimensions and at typical temperatures, conductors have lower resistance than insulators.

• For most conductors, resistance increases with temperature,

• For semiconductors, the resistance decreases with temperature,

• For insulators, their resistance may do either.

• At very low temperatures some materials called superconductors have zero resistance

• These are the resistances at low voltages.

• At sufficiently high voltage across small distances, all materials (even empty space) become good conductors.

• The voltage at which this occurs is called the breakdown voltage.

  • For air the breakdown voltage is 3 MV/m, for glass ~10 MV/m, for diamond it is 2000 MV/m, and for a vacuum 1012 MV/m.

Electric Safety

• It is not voltage that is dangerous, it is current.

  • Remember voltage is related to potential energy. A high voltage is similar to standing on top of a mountain.

  • A current of 0.01 A is very painful, and 0.1 A can be fatal.

  • Household outlets have a potential of 120 V.

  • For a given voltage drop, the current increases as the resistance decreases.

  • The typical resistance of the human body is ~100,000 ohms but just ~100 ohms when it is wet. If the current flowing through an appliance finds it easier to reach ground through your body the current through you will be ~0.001 A if your skin is dry but ~1 A if it is wet.

  • Electricity and water are a very bad mixture

EXAMPLE 1:

What is the current through a 10 ohm resister connected to a 120 V power supply?

• V = IR > I = V/R > I = 120 V / 10 ohms

• I = 12 amps

AC/DC

• When the voltage difference between two points is fixed the current always flows in the same direction.

• A current that always flows in the same direction is called a direct current which is abbreviated as dc. There are some voltage sources where the voltage difference between two points alternates from negative to positive.

  • Here in the US, the voltage switches 60 times a second i.e. 60 Hz.

• The constant switching of the potential difference causes the current to also switch directions. Such currents are called an alternating current which is abbreviated to ac.

  • in addition to their regular dc resistance, materials have a different kind of resistance to ac known as a reactance that doesn’t heat the material.

  • Reactance changes with the frequency of the alternations.

Electric Power

• When a current flows, electrical potential energy of a charge is being converted into kinetic energy of the charge.

• The kinetic energy of electric charges is what is usually called electrical energy.

• Some of the kinetic energy is converted into heat due to resistance along the path of the current.

  • this kind of heating is called Joule heating or Ohmic heating.

  • Ohmic heating is proportional to the square of the current.

  • Power Lost=(Current) ^ 2×Resistance

• What isn’t lost to heat can be used to do something useful.

• The rate at which the electrical potential energy is converted into other forms of energy is the electrical power.

  • Power= Potential energy / time interval

• Remember:

  • Potential energy=Charge×Voltage

  • Current= Charge moved / time interval

• Putting these together we find

  • Power=Current×Voltage

• As before, the unit of power is the watt, symbol W

Electric Circuits

An electric circuit is a voltage source plus one or more circuit elements continuously connected so as to allow a current to flow between the voltage source terminals. Circuit elements are various devices such as:

• wires

• switches,

• capacitors,

• resistors,

• diodes

There is a lot of similarity between electric circuits and hydraulic circuits.

• Each circuit element is represented by a symbol in a circuit diagram – a schematic diagram of the circuit.

Switches and Fuses

• A (direct) current only flows if there is a continuous path for the charge to flow between the terminals of the voltage source.

• A switch is a simple device to create gaps in a circuit.

• Current flows when the switch is closed, when it is open no current flows.

• A fuse is a thin piece of wire that melts when the current through it becomes too large.

  • fuses create gaps in the path of the current when they blow.

  • fuses are rated by the amount of current flowing before they blow.

• Larger than expected currents occur when the resistance of a device drops (typically because the device short circuits).

• A fuse needs to be replaced when the wire blow: circuit breakers are similar to fuses but can be reset when tripped.

Diodes

• Many electrical devices do not work with ac, they need dc.

  • your computer is one example.

• Converting ac to dc is called rectification.

• Diodes are circuit elements that only allow current to flow in one particular direction.

  • light-emitting diodes (LEDs) are special diodes that emit light.

• Modern diodes are made from semiconductor materials such as silicon, sometimes germanium

  • diodes were the first semiconductor devices

• A single diode will remove half the current.

• Arrangements of several diodes called bridge rectifiers reverse the current without removing any of it

  • capacitors are included in the design to smooth the current

Series and Parallel Circuits

• Circuits come in two basic designs: series and parallel.

• A series circuit is one where the current has only one path between the terminals of the voltage source.

• A parallel circuit is one where the current has two or more paths between the terminals of the voltage source.

• A series circuit would be a battery, a switch and three lights such that the current has to flow through all the bulbs.

• If there is a gap anywhere in the circuit, no current flows.

• The current is determined by the total resistance.

• The resistance of the circuit is the sum of the resistances of each circuit element.

• There is a voltage drop across each element and the sum of each voltage drop equals the voltage source.

• A parallel circuit would be a battery and three lightbulbs such that the current divides and can flow through only one bulb.

• If there is a gap in one of the paths, current still flows.

• The voltage drop across each element is the same for each.

• The current splits to go through each branch with the current in a particular branch inversely proportional to the resistance through that branch.

• The resistance of the circuit is less than the resistance of each circuit element (so less than the smallest).

EXAMPLE 1:

How does the resistance of a circuit change when two identical lamps in a circuit are connected in parallel?

• It decreases.

  • Circuit branches in parallel are like extra lines at a checkout: more lines means less resistance, allowing for more flow.