Short answers, pulled from the story.
Electrical resistance measures how strongly an object opposes the flow of electric current, while conductance measures how easily current passes through. The two are reciprocals of each other: as resistance increases, conductance decreases by the same factor. Resistance is measured in ohms and conductance in siemens.
Ohm's law states that the current through a material is directly proportional to the voltage applied across it, keeping resistance constant over a wide range of voltages and currents. Materials that satisfy this relationship are called ohmic; wires and resistors are common examples. Diodes, fluorescent lamps, and batteries are non-ohmic and do not follow Ohm's law.
Resistance is proportional to the length of a conductor and inversely proportional to its cross-sectional area. A long, thin wire has higher resistance than a short, thick wire made of the same material. These are extensive rather than intensive properties, meaning they change with the geometry of the object, not just its material.
Joule heating is the conversion of electrical energy to thermal energy that occurs whenever current flows through a resistance, named after James Prescott Joule. It is the operating principle of electric stoves, resistive heaters, and incandescent lamps, where the filament is heated until it glows white hot. The same effect causes unwanted energy losses in power transmission lines.
Superconductors have exactly zero resistance and infinite conductance, meaning current can flow through them indefinitely without any energy loss. Most metallic superconductors such as niobium-tin alloys require cooling to near 4 kelvin using liquid helium, while ceramic high-temperature superconductors operate near 77 kelvin and use liquid nitrogen.
Near room temperature, the resistivity of metals typically increases as temperature rises, while the resistivity of semiconductors typically decreases. A linear approximation using the temperature coefficient of resistance is commonly applied when temperature does not vary too much; for metals near room temperature this coefficient is typically in the range of positive 3 to 6 thousandths per kelvin. Devices that exploit this temperature dependence intentionally are called resistance thermometers, made of platinum, or thermistors, made of ceramic or polymer.