Electricity
Elementary charge
The elementary charge e is the smallest possible unit of charge. It is the charge of a single proton or electron, measured in coulombs. Protons have a charge +e, and electrons have a charge of -e.
Conversely, the number of electrons in 1 coulomb is 1.6\e{19}.
The charge Q of an object is equal to the difference in the number of protons n to the number of electrons m, times the elementary charge e. This charge must be a multiple of e.
Conservation and movement of charge
Charge is always conserved in an isolated system. Electrons move around, but are never created or destroyed.
Electrons in an insulator are tightly bound and can’t travel.
Coulomb’s law
The electrostatic force between two charged bodies is proportional to the product of the charges q_1 and q_2, and is inversely proportional to the square of the distance r between the bodies. If the force is positive, the bodies repel each other, and if the force is negative (q_1 and q_2 have opposite signs) they attract.
The constant k is equal to 9\e{9} \unit{Nm}^2 \unit{C}^{-2}.
The electrostatic force is very similar to the gravitational force, but is a lot stronger over small distances.
Charges of the same polarity repel, and charges of opposite polarities are attracted to each other. When two objects touch, electrons move between the two until the charges of the objects are equal.
Electric fields
The strength of an electric field is given by the following equation, where E is field strength in NC^{-1} or Vm^{-1}, q is charge in coulombs, d is the distance across which voltage was measured, and F is the force in newtons imparted to a charge in the field.
When drawing a diagram, the field lines point from the positive end to the negative end. Electrons move against these lines, protons move with (because opposites attract).
An electric field can be blocked by a conductor, because the electric field strength inside a conductor is zero.
Work done on a charge
A similar equation can be derived from the above, where the work W in joules (which is the same as the electric potential energy U_e) is given by the potential difference across the field and the size of the charge to be moved.
“A charged particle in an electric field has electric potential energy.” Moving a charge against a potential difference requires energy, and conversely, a charge is moved by a potential difference. The amount of energy required to move a charged particle from A to B is determined by the difference in potential energy between those two points:
Positive charges move in the direction of the field lines (from positive to negative).
A voltage source gives e \times V joules of energy to each electron flowing through the circuit (because U_e = Vq). That is, voltage turns into electric potential energy per unit charge.
Current
Current moves from a positive potential to a negative potential (same as the lines of an electric field diagram). Electrons move in the opposite direction (negative to positive, because opposites attract).
Current is the flow of positive energy.
Resistance
Resistance of a material depends on cross-sectional area A, the length of the material l, and resistivity \rho. It is caused by electrons bouncing off other electrons and positive ions.
Energy is dissipated by a resistor / by doing work.
Power
Energy is proportional to power and time.
Kirchoff’s laws
Kirchoff’s voltage law
AC current
root mean square