#### xaktly | Electricity & Magnetism

Electric current

Electric current is strongly related to electric potential (also called "voltage", electric resistance, and electric charge. To understand one, you'll need to understand all of them, so make sure to visit all of those pages.

### Electric current

Electrict current is a measure of the flow of charged particles past some point. Usually we're talking about current in wires and the charged particles are electrons. That doesn't have to be the case, though. We might easily measure the current of a beam of protons through air (or even better, a vacuum).

Charged particles can be electrons, protons or ions – any particle with a charge.

And the medium – what the charges are moving in – can be a wire, a solution, air, vacuum — whatever a charge can move in.

The flow of electric current through neurons is an ion current, a rapid motion of positive and negative ions back and forth across a membrane. That pulse of back-and-forth motion transmits a signal along the length of a nerve cell, which is long and thin, like a wire.

### Units of charge and current

We reference the measurement of all electric charges to that of the electron, and we define one Coulomb of charge (abbreviated C) as the total charge on 6.241 x 1018 electrons. That means that the charge carried by one electron is the reciprocal, about 1.602 x 10-19 C. The crazy number of electron charges in the Coulomb is a result of the fact that early scientists defined the measure of electric current first, the Ampere.

... Hey, it's easy to coach the game after it's been played.

The Ampere (A or "amp") is the customary unit of current. It is defined as the passing of 1 Coulomb (1 C) of charge in 1 second. A 5 A current through a wire means that 5 C of charge are passing the measurement point every second.

Unit of electric charge: 1 Coulomb (C)

1 Coulomb = amount of charge present on 6.231 × 1018 electrons.

Unit of electric current: 1 Ampere (A)

1 Ampere = 1 C of charge passing a point per second: 1 A = 1 C/s

### Conductors & Insulators

Most often when we think of electric current, we think of current in wires. Metals like copper, silver and gold are very good conductors of electricity, that is, electrons may flow freely in those and most other metals because of how electrons are arranged around their nuclei.

Other materials, like most plastics and ceramics, glass, rubber and teflon behave in the opposite way. Their electrons are held so tightly to their atoms that there are just no electrons free to move inside the material; they won't carry a current. These materials, like the plastic coatings on the wires shown, are insulators.

#### Other carriers of current

Electrons are not the only carriers of electric current. Many important electric currents, including the currents along the nerve fibers in your brain and body at work right now, are propagated by ions, atoms or molecules that contain more or fewer electrons than the number of protons, so they have a non-zero charge.

### Mythbusting: Water as a conductor

Pure water is a terrible conductor of electricity. In fact, we often measure the purity of water in laboratories that need high purity in terms of its inability to carry electric current.

This can be illustrated by using water to complete a circuit (between the black and red wires) like this:

For pure water, only an exceedingly small current will flow because there's just not enough charged material dissolved in the liquid.

On the other hand, if we add some soluble ionic salt, like sodium chloride (NaCl), which breaks apart in water into sodium (Na+) and chloride (Cl-) ions (see below), we find that the water can carry a significant current.

To varying degrees, natural waters carry current. Sea water, with its high concentration of dissolved salts, is the best of these. Yet even when lightning, which carries a tremendous current, impacts the sea surface, the current rapidly dissipates as it spreads out.

This figure shows how highly-ordered crystals of positively-charged sodium ions and negatively-charged chlorine (called chloride) ions of sodium chloride (NaCl, or table salt) break apart when dissolved in water to create ions that can move in the solution and therefore carry current.

Ions carry current in many important systems. Animal nerve cells, for example, use a combination of simple ions like Na+, K+ and Cl- to propagate nervous impulses along a chain of neurons at very high speed.

### Electric circuits

In order for any electric current to flow, it must complete a circuit of some kind. Let's take a look at the simplest kind of circuit (right), then build in some extra features later.

We need only two things to make the simplest circuit, a source of current (from now on we'll assume that's a source of electrons) and a wire.

For our purposes for a while, we'll use a battery as a source of electrons. Batteries make use of a special kind of chemical reaction called an oxidation-reduction (or "redox") reaction to liberate electrons from certain molecules.

Because nature requires a balance of charges, however, electrons leaving the battery at one end must be replaced at the other.

Well, that's a boring circuit. It doesn't do anything except maybe heat up the wire and drain the battery. We build circuits to run motors, power lights or carry signals in digital computers, or any number of other applications.

#### A circuit that does something

Here is a circuit that lights an incandescent bulb. Trace the path of the current. It goes through the coiled part of the lightbulb, the filament, which is usually a very thin piece of wire that is a little more resistant to the flow of electrons than the rest of the wire.

Current is forced through this "choke point" so hard by the battery that the electrons experience a lot of friction, move very rapidly, and occasionally jump right off the wire because they gain so much extra energy. When these electrons reattach to the wire (they don't go far), they have to lose all of that energy, and they lose it - or radiate it - in the form of light.

This same principle is at work when we heat up the burner on an electric stove. It doesn't get nearly as hot as the filament on a lightbulb, just enough to glow red heat soup.

### Resistance

In the lightbulb circuit, we said that the bulb is a "choke point" for electrons, and that brings up an interesting point: Not every substance or metal can accommodate the same amount of electric current. Different substances resist the flow of current to varying degrees. Insulators completely resist the flow of current and wires hardly resist it at all, but there are a host of materials with in-between properties. This property is known as resistance.

The unit of resistance is the Ohm, which we abbreviate with the Greek lower case letter omega (the last letter of the Greek alphabet), Ω — like a horseshoe.

The table below lists the resistivity, in Ω·m, of several materials. Notice that the resistivity of typical metal conductors is very low (~10-9 Ω), while that of insulators is very high (~108 Ω). Resistance is obtained by multiplying the length of the material by the resistivity; the longer the path of electrons through any substance, the higher the resistance.

In between lie an important class of materials like silicon, germanium and arsenic, which are semiconductors. These can be coaxed into carrying current or not, and form the basis of digital computing and electronics.

Most metals are excellent conductors. Gold is particularly good because it has a very low resistance and because it doesn't oxidize (corrode) easily in air.

##### Resistivities of selected materials
Material Resistivity / Ω·m
Silver (Ag) 0.0000000159
Copper (Cu) 0.0000000168
Graphite (C) 0.000035
Silicon (Si) 0.1 – 60
Glass 1,000,000,000
Hard rubber 1012

Silicon is a semiconductor. Depending on what's added to it, it can either conduct current or insulate. It's the basis for the semiconductor industry.

Glass, plastics and ceramics have extremely high resistance to the flow of current, so they're used as insulators in places where we want no current to flow.

X

#### The Greek alphabet

 alpha Α α beta Β β gamma Γ γ delta Δ δ epsilon Ε ε zeta Ζ ζ eta Η η theta Θ θ iota Ι ι kappa Κ κ lambda Λ λ mu Μ μ nu Ν ν xi Ξ ξ omicron Ο ο pi Π π rho Ρ ρ sigma Σ σ tau Τ τ upsilon Υ υ phi Φ φ chi Χ χ psi Ψ ψ omega Ω ω

The unit of resistance to the flow of electron current is the Ohm, Ω.

$$1 \Omega = 1 \; \frac{Kg \, m^2}{s^3 A^2}$$

Resistance is a property of any material. In general the resistance of conductors is low and the resistance of insulators is high.

This Intel processor chip uses gold-plated connectors for maximum conductivity and resistance to corrosion. →

Computer recyclers recover the gold from junked computers, but the coating is very thin (about 0.4 micrometers).

In the next few sections you can learn more about batteries and electric potential ("voltage") and resistance, then you can put that knowledge together in circuits.

### Ohm's law

#### Relationship between current, potential and resistance

Above, we called a battery a "source of electrons." It's actually a little more than that. You might think of a battery as an electron "pump." The higher the voltage (better known as potential) of the battery, the more force it has to pump electrons through a conductor.

The relationship between potential [measured in Volts (V)], current and resistance is Ohm's law,

#### V = IR,

where V is voltage in Volts (V), I is current in Amperes (Amps, A) and R is resistance in Ohms (Ω).

In useful electric circuits, we're manipulating current and potential by changing resistance and by other means. Ohm's law allows us to calculate current, potential or resistance if we know the other two quantities.

### Practice problems

 1 A potential of 4.5 V is placed across a wire containing a 500 Ω resistor. Calculate the resulting current through the wire. Solution We use Ohm's law, V = IR, and rearrange it to find the current: \begin{align} I &= \frac{V}{R} \\[5pt] &= \frac{4.5 \, V}{500 \, \Omega} \\[5pt] &= 0.009 \, A \\[5pt] &= 9 \, mA \end{align} It's common to express currents of less than 1 A in terms of milliamps (1 mA = 0.001 A). 2 The current through a circuit is measured to be I = 0.400 A (400 mA) when the voltage or potential "driving" the circuit is 13.5 V. Calculate the resistance of the circuit. Solution We use Ohm's law, V = IR, and rearrange it to find the resistance: \begin{align} R &= \frac{V}{I} \\[5pt] &= \frac{13.5 \, V}{0.4 \, A} \\[5pt] &= 33.75 \, \Omega \end{align} 3 A 2.5 MΩ (1 MΩ 1 mega Ohm = 106 Ω) resistor has a current of 0.350 A running through it. Calculate the potential across the resistor. Solution We use Ohm's law, V = IR to find the voltage: \begin{align} V &= IR \\[5pt] &= (0.350 \, A)(2.5 \times 10^6 \, \Omega) \\[5pt] &= 875,000 \, V \\[5pt] &= 875 \, KV \end{align} It's customary to express potentials greater than 999 V in terms of kilovolts (1 KV = 1000 V).
 4 How much current is running through a circuit in which 100 C of charge pass by a point of measurement every second? Solution Current is defined as the number of Coulombs of charge passing a point each second, so the current here is $$I = \frac{q}{t} = \frac{100 \, C}{1 \, s} = 100 \, A$$ Note: That's actually a huge current. In order not to melt a circuit, the voltage producing this current would have to be very low. 5 How much current is running through a circuit if 100,000 electrons pass a point every second? The charge of 1 electron is 1.602 × 10-19 C. Solution 100,000 electrons at 1.602 × 10-19 C per electron is $$10^5 \times 1.602 \times 10^{-19} = 1.602 \times 10^{-14} C$$ So the current (dividing the charge by 1 second) is 1.602 × 10-14 A. You can see that larger currents represent the passage of huge numbers of electrons. 6 How long does it take for 15 Coulombs of charge to pass a point in a circuit if the current (rate of flow) is 1.7 A? Solution All we need is the definition of current, $$I = \frac{q}{t},$$ where q is charge and t is time. Rearranging gives us $$t = \frac{q}{I} = \frac{15 \, C}{1.7 \, A} = 8.82 \, s$$

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