Electrical engineering: TestAS practice testlets

In an electric circuit, a voltage source such as a battery drives a current through conductors and components. Ohm's law states that the current I through a resistor is proportional to the voltage U across it: U = R·I, where R is the resistance in ohms (Ω). The electrical power converted in a component is P = U·I.

U = R·I P = U·I series: R = R1 + R2 parallel: 1/R = 1/R1 + 1/R2

Components can be connected in series or in parallel. In a series connection, the same current flows through all components, the voltages across them add up to the source voltage, and the total resistance is the sum of the individual resistances. If one component fails and breaks the circuit, the current stops everywhere, as in old strings of Christmas lights.

In a parallel connection, all components have the same voltage across them, the currents through them add up to the total current, and the total resistance is smaller than the smallest individual resistance. Household appliances are connected in parallel, so that each receives the full mains voltage and can be switched independently. These rules follow from Kirchhoff's laws: at any junction, the sum of currents flowing in equals the sum flowing out (junction rule), and around any closed loop, the voltages add up to zero (loop rule).

The more appliances are switched on in parallel, the smaller the total resistance and the larger the total current. Fuses and circuit breakers interrupt the circuit when the current exceeds a safe value, to prevent wires from overheating.

A technician tests two arrangements of the same two resistors, R1 = 4 Ω and R2 = 6 Ω, connected to a 12 V battery whose internal resistance can be neglected.

Measuring instruments must be connected correctly. An ammeter, which measures current, is connected in series with the component, so that the same current flows through it, and it has a very low resistance. A voltmeter is connected in parallel with the component whose voltage it measures and has a very high resistance, so that it draws almost no current. Connecting an ammeter in parallel with a battery would cause a short circuit and could destroy the instrument. In practical calculations, engineers usually simplify a circuit step by step, replacing series or parallel groups of resistors by their equivalent resistance until only one remains.

Electric current is the flow of electric charge. Its unit, the ampere (A), corresponds to a charge of one coulomb passing a point per second. A voltage, measured in volts (V), is the energy transferred per unit of charge; it drives the current through a circuit. The resistance of a component, in ohms, determines how much current flows for a given voltage (Ohm's law, U = R·I). The resistance of a wire increases with its length and decreases with its cross-sectional area, and it depends on the material: copper and aluminium conduct well, which is why they are used in cables.

P = U·I E = P·t R = ρ·l ÷ A 1 kWh = 1,000 W × 3,600 s

In Europe, household sockets supply an alternating voltage of about 230 V. Every appliance is labelled with its power rating in watts: the power P, the energy converted per second, equals voltage times current. A kettle rated at 2,300 W therefore draws a current of 10 A. The energy used over a period is power times time. Electricity suppliers bill energy in kilowatt-hours: an appliance with a power of 1 kW running for one hour uses 1 kWh, which is 3.6 million joules.

Household circuits are protected by circuit breakers or fuses, typically rated at 16 A. If the total current in a circuit exceeds this value, for example when several powerful appliances run on the same circuit, the breaker trips to prevent the cables from overheating. A residual-current device additionally compares the current flowing out and back; if some current leaks away, for instance through a person touching a faulty appliance, it switches off within a fraction of a second.

Electric charges exert forces on each other. Like charges repel and unlike charges attract. According to Coulomb's law, the force between two point charges is proportional to the product of the charges and inversely proportional to the square of their distance: doubling the distance reduces the force to a quarter. This force holds atoms and molecules together and is responsible for static electricity.

Many devices consume energy even when switched off but still plugged in, a phenomenon known as standby consumption. Although each device uses little power, the total can amount to a noticeable share of a household's electricity bill.