# Electricity

In 1799 Alessandro Volta is credited with building the first electric battery. Volta's battery produced voltage with an electrolyte sandwiched between two different metals.

In 1831 Michael Faraday discovered that voltage is produced by moving a magnet past a wire. Coal, gas, nuclear, hydroelectric, and geothermal power plants all produce electricity by moving magnets past wires.

Solar panels are growing in popularity as an alternative voltage source. They use the photovoltaic effect to convert light into electricity. Albert Einstein explained the photovoltaic effect in 1905, but it wasn't until the 1950s that Bell Laboratories developed the first solar panels.

## Electric Current

Voltage sources produce electric current in conductors. Electric current is the average motion of a huge number of charges through a conductor. The electrons don't just move in a straight line. They drift through the conductor in a random walk bouncing off other charges.

These simulations model electric current with Coulomb's law. They don't include the nuances of quantum mechanics.

A small imbalance in net charge produces an electric field. The electric field points in the same direction as the current.

In 1746 Benjamin Franklin mistakenly assigned a negative value to the charge carriers that we now call electrons. This annoying choice set a precedent that made the direction of electric current opposite of the direction the electrons actually move.

Negative charge flows away from negative potential and towards positive. Positive charge does the opposite.

Question: What direction is the current in the above simulations?

Current is flowing to the left.

Current is defined as the flow of positive charge. We see the electrons move to the right, but they have negative charge. The current is in the opposite direction of the electron flow.

Question: Why do the electrons move, but not the nuclei?
answer $$\text{electron} = 9.1 \times 10^{-31} \, \mathrm{kg}$$ $$\text{copper nucleus} = 1.0 \times 10^{-25} \, \mathrm{kg}$$

An electron is about 10 000 times lighter than a typical nucleus. This means forces experienced by electrons will produce larger accelerations and larger velocities.

Additionally, the nucleus and the lower electron shells are strongly held in place by the metallic bonds. Metallic bonds are formed when the outer electron shells are shared between nuclei. This outer electron shell forms a conductive layer in metals.

The average flow of electrons in a typical wire is around 0.0002 m/s.

Question: If the flow of electrons is slow, why isn't there a delay in the music coming out of my headphones? Why is communication by phone, TV, and internet near instantaneous?

In conductors, an imbalance in electric charge for one atom will cause nearby atoms to have the same imbalance. Changes in this imbalance of charge spread as a wave at near the speed of light. Electric signals are waves in the electric field.

The electrons aren't the signal. The signal is the changes in the electric and magnetic field.

Current measures the flow of charge over a period of time. Current is not a substance. Current is a rate, like dollars per hour is a rate.

# $$I = \frac{q}{\Delta t}$$

$$I$$ = electric current [A, amps, amperes, C/s]
$$q$$ = charge that passes a point on a wire [C, coulombs]
$$\Delta t$$ = a period of time [s]

It can be helpful, and accurate, to think of electric current like water current. Free electrons flow through metals like H₂O flows through pipes.

Example: 1.2 coulombs of charge passes through a typical LED every minute. What is the current in the LED?
solution $$I = \frac{q}{\Delta t}$$ $$I = \frac{1.2\, \mathrm{C}}{60\, \mathrm{s}}$$ $$I= 0.02 \, \mathrm{\tfrac{C}{s}}$$ $$I= 0.02 \, \mathrm{A}$$
Example: Two wires of cross-sectional area 1.6 mm² connect the terminals of a battery to the circuitry in a clock. After 0.04 seconds, 5.0 × 10¹⁴ electrons move through a point on the wire. What is the current in the wires?
strategy

Build a conversion fraction to convert 1 electron into electric charge. Use the charge and the time to calculate the current.

solution $$q = 5.0 \times 10^{14} \, e^{-} \left(\frac{1.6 \times 10^{-19} \, \mathrm{C}}{1 \, e^{-}}\right) = 0.00008\, \mathrm{C}$$
$$I = \frac{q}{\Delta t}$$ $$I = \frac{0.00008\, \mathrm{C}}{0.04 \, \mathrm{s}}$$ $$I = 0.002 \, \mathrm{A}$$
Example: If 0.320 mA of charge flow through a calculator, how many electrons pass through per second?
solution $$I = \frac{q}{\Delta t}$$ $$q = I\Delta t$$ $$q = (0.320 \times 10^{-3}\, \mathrm{A}) (1\, \mathrm{s})$$
$$q = 0.000320 \, \mathrm{C} \left(\frac{1 \, e^{-}} {1.6 \times 10^{-19}\, \mathrm{C}}\right)$$ $$q = 2 \times 10^{15} \, e^{-}$$

## Voltage (Potential Difference)

Voltage is a measure of the difference in electrical potential between two points. Voltage is defined so that negative charges are pulled towards positive potential, and positive charges are pulled towards negative potential.

The two terminals in a wall socket are sources of voltage. The positive and negative terminals on a battery also provide voltage.

These simulations model a "circuit" with a "battery". The battery pushes the negative charges down, which produces a difference in electric potential.

Areas with more negative charge have negative potential.
Areas with more positive charge have positive potential.

Question: Why does only the right simulation produce a flow of charges.

When the circuit isn't connected electric charge builds up at each end point. Connecting the ends to form a loop guides the charges back to the start to complete another cycle.

Measure: Let each sim run until they settle on a voltage. Record that voltage.
results

The left simulation has a voltage around 7.2 V.
The right simulation has a voltage around 4.6 V.

Follow Up Question: Why is the voltage lower for the circuit on the right?

Connecting the ends of the circuit gives the charges a conductive path. This path allows some of the built up potential to equalize.

Electric circuits have either direct current or alternating current depending on the source of the voltage.

In DC (direct current) circuits, a constant voltage source pushes the electrons around the circuit in one direction. Batteries are common source of DC.

In AC (alternating current) circuits, a rapidly changing potential pushes the electrons forward and backwards about 60 times a second. A wall socket is a source of AC.

Question: Predict what happens to the flow of electrons after adding resistors.

Adding more resistors will cause the electron's average forward progress to be slower because the resistors cause "traffic jams".

Question: What would happen if we removed all the resistors?

Removing most of the resistance in a circuit leads to a short circuit. This causes the average electron flow to increase, producing dangerous amounts of heat.

A DC voltage source is represented by one or more pairs of lines.

The longer line in the symbol represents the positive terminal, and it is called the cathode. The shorter line is the negative terminal, called the anode. Electrons flow out of the anode, but the current is defined as coming out of the cathode.

Question: What's an example of a DC voltage source?

Batteries, solar panels, and DC motors are DC voltage sources.

Wall sockets are sources of AC voltage.

## Ohm's Law

In 1827, German physicist Georg Ohm published his work on the relationship between electric current and voltage. Ohm discovered his law after measuring the voltage on wires of different length. He found that as wires got longer they had less current for the same voltage.

Ohm's Law says that the voltage in a conductor is proportional to the current. This means we can build an equation where V = I times a constant. The constant is called resistance and it measures how current responds to a change in voltage.

The resistance of a material is the inverse of its conductivity. Conductors have nearly zero resistance and insulators have very high resistance.

# $$V = IR$$

$$V$$ = voltage, a change in electric potential [V, volts]
Technically ΔV, but V is often used for simplicity.

$$I$$ = electric current [A, amps, amperes]

$$R$$ = resistance [Ω, ohms]

This form of Ohm's law is for direct current circuits only.

Circuit elements convert electric potential into other types of energy. LEDs make light. Electric motors make motion. Electric speakers make sound. Logic circuits perform calculations.

Any element of a circuit that does something will cause the electric potential to drop and add resistance to the circuit.

Play with this circuit simulator for resistance. Adjust the wiggle of the resistor to see how it changes the voltage and current.

Semiconductive elements, called resistors, have more resistance than a metal wire, but still much less resistance than an insulator, like air or plastic.

Resistors are added to a circuit for precise control over current. If the current is too high, the circuit will get hot. If the current is too low the circuit can't do its job.

The IEC symbol for a resistor is this rectangle.

The American representation of a resistor is this squiggle, which I use because I like the way it looks.

A pipe with flowing water is analogous to a wire with flowing charge.

A wire is like a water pipe.
An electric charge is like a water molecule.
A battery is like a water pump.
Electric current is like water flow.
Electric potential is like water pressure.

Question: What would a resistor be in this analogy?

A resistor slows down the flow (current), and drops the pressure (potential). In a water pipe a resistor would be a narrowing of the pipe, or a partial clog.

Example: Find the voltage for a resistor that has 300 Ω of resistance and a current of 0.05 A.
solution $$V = IR$$ $$V = (0.05\, \mathrm{A}) (300 \, \Omega)$$ $$V = 15 \, \mathrm{V}$$
Example: Find the current for a 100 Ω resistor with 2 V drop?
solution $$V = IR$$ $$I = \frac{V}{R}$$ $$I = \frac{2 \, \mathrm{V}}{100 \, \Omega}$$ $$I = 0.02\, \mathrm{A}$$
Example: If I double the voltage in a circuit while keeping the resistance the same, what happens to the current?
solution

Resistance is constant so we can just pretend it is one.

$$V=IR$$ $$V=I$$ $$2V=2I$$

Voltage and current are directly proportional. Doubling V will double I.

resistance = Ω

Question: What is the relationship between resistance, current, and voltage?

For constant resistance:
When voltage is increased, the current is __________.
When voltage is decreased, the current is __________.

When voltage is increased, the current is increased.
When voltage is decreased, the current is decreased.

Voltage and current are directly proportional.
They increase and decrease together.

For constant voltage:
When resistance is increased, the current is __________.
When resistance is decreased, the current is __________.
solution $$V = IR$$ $$R = \frac{V}{I}$$ $$R = \frac{1.5\, \mathrm{V}}{0.001\, \mathrm{A}}$$ $$R = 1500 \, \Omega$$
solution $$I = \frac{q}{\Delta t}$$ $$I = \frac{0.02}{10}$$ $$I = 0.002 \, \mathrm{A}$$
$$V = IR$$ $$V = (0.002)(10)$$ $$V = 0.02 \, \mathrm{V}$$