Charge, current, and voltage
Electrical engineering begins with three ideas: electric charge, the flow of charge called current, and the energy per charge called voltage. Every circuit, from a torch to a supercomputer, is built on them.
Electric charge
Charge is a fundamental property of matter, measured in coulombs (C). Electrons carry a negative charge of about \(1.602 \times 10^{-19}\) C each, and protons an equal positive charge. Like charges repel and opposite charges attract. Charge is conserved: it can move but is never created or destroyed. One coulomb is the charge of about \(6.24 \times 10^{18}\) electrons.
Current
Current is the rate at which charge flows past a point: \(i = \frac{dq}{dt}\), measured in amperes (A), where 1 A is 1 coulomb per second. By convention, current direction is the direction positive charge would move, from higher to lower potential through a load, even though in metal wires the moving charges are electrons travelling the opposite way. Direct current (DC) flows steadily in one direction; alternating current (AC) reverses periodically.
Voltage
Voltage, or potential difference, is the energy per unit charge needed to move charge between two points: \(v = \frac{dw}{dq}\), measured in volts (V), where 1 V is 1 joule per coulomb. A battery maintains a voltage between its terminals, pushing current through a circuit. Voltage is always measured between two points; a single node's voltage is quoted relative to a chosen reference, ground.
Power and energy
Power is the rate of energy transfer: \(p = vi\), in watts (W). With passive sign convention, current entering an element's positive terminal, positive power means the element absorbs energy, as a resistor or charging battery does; negative power means it supplies energy. Energy is power integrated over time, often billed in kilowatt-hours: 1 kWh is \(3.6 \times 10^{6}\) J.
Circuit elements
A circuit is an interconnection of elements forming closed paths for current. Sources supply energy: independent voltage sources maintain a set voltage, and independent current sources maintain a set current, whatever else is connected. Passive elements, resistors, capacitors, and inductors, absorb or store energy. Dependent sources, controlled by another voltage or current, model transistors and amplifiers.
Nodes, branches, and loops
A branch is a single element or path; a node is a point where two or more branches connect; a loop is any closed path through the circuit. Wires in circuit diagrams are idealised as having zero resistance, so all points connected by plain wire are the same node. Identifying nodes and loops correctly is the first step of every circuit analysis.
Units and prefixes
Engineering values span many orders of magnitude, so SI prefixes are used constantly: pico (p, \(10^{-12}\)), nano (n, \(10^{-9}\)), micro (\(\mu\), \(10^{-6}\)), milli (m, \(10^{-3}\)), kilo (k, \(10^{3}\)), mega (M, \(10^{6}\)), and giga (G, \(10^{9}\)). A 4.7 k\(\Omega\) resistor is 4,700 ohms; a 100 nF capacitor is \(10^{-7}\) farads; a 20 mA LED current is 0.02 A.
Worked example
A phone charger delivers 5 V at 2 A. Power is \(p = 5 \times 2 = 10\) W. Charging for 1.5 hours transfers \(10 \times 1.5 = 15\) Wh of energy, which is \(15 \times 3600 = 54{,}000\) J. The charge delivered is current times time: \(2 \times 5400 = 10{,}800\) C, equal to 3,000 mAh, the way battery capacity is usually quoted.
Key takeaways
Charge, in coulombs, is conserved; an electron carries about 1.602 x 10^-19 C. Current is the rate of charge flow, i = dq/dt, in amperes, with conventional direction opposite to electron motion. Voltage is energy per charge, in volts, measured between two points relative to a reference. Power is p = vi in watts; passive sign convention tells absorbed from supplied power; 1 kWh = 3.6 MJ. Circuits contain independent and dependent sources and passive elements, analysed via nodes, branches, and loops. SI prefixes from pico to giga express values compactly.
Flashcard
Unit of charge
Check your understanding
A device draws 0.5 A from a 12 V supply for 2 hours. How much energy does it use?