CURRENT | CURRENT DENSITY | ELECTRIC POTENTIAL | ELECTRIC POTENTIAL DIFFERCE | VOLTAGE
Electric current is simply the flow of electric charge. In most practical circuits the moving charges are electrons, and current is what powers lights, motors and all electronic devices. The standard unit is the ampere (A). One ampere means one coulomb of charge passing a point every second.
Think of current like water flow in a pipe: more water passing a cross-section per second equals higher flow. That analogy helps explain how changing the pipe size, pressure or obstacles changes the flow — similar to wires, voltage and resistance for electricity.
Current density (J) tells how much current flows per unit area of a conductor's cross-section. If current is the water, current density is how concentrated that water is in a small part of the pipe. Mathematically, J = I / A, where I is current and A is area.
Higher current density can lead to heating and damage — that’s why cables have rated ampacity. A practical tip: if you need to double current without overheating, either double the conductor area (thicker wire) or split the current across parallel conductors.
Electric potential (often just called potential) at a point is the potential energy per unit charge. It tells what energy a unit positive charge would have at that point. Units are volts (V), which are joules per coulomb.
Use an everyday mental model: imagine a hill and a marble. The height of the hill corresponds to potential. A marble at the top has more potential energy than at the bottom. Similarly, a positive charge at higher potential has more electrical potential energy compared to a lower potential point.
Potential difference between two points is what we call voltage — it’s the difference in potential energy per unit charge. Voltage is the 'push' that makes charges flow when there is a closed path: the greater the voltage, the stronger the push.
Ohm's law (V = IR) connects voltage (V), current (I) and resistance (R). Remember: if you increase V, you increase I (for a fixed R). If you increase R, current goes down for the same V.
1 — Quick unit checks: Current (A), Current density (A/m2), Potential (V), Energy (J). If units don't match, something's off.
2 — Wire sizing rule of thumb: For small hobby circuits use 22–24 AWG for up to 0.5–1 A, 18 AWG for a few amperes, and 14 AWG+ for household currents. Always check real ampacity tables when in doubt.
3 — Visualize with water: Voltage ~ pressure, Current ~ flow, Resistance ~ narrowness/friction. This keeps equations like V = IR intuitive.
4 — Spot heating early: If a cable or connector gets warm to touch, current density or contact resistance is too high — reduce current or improve connections.
Below is a ready-to-download PDF with summarized formulas, diagrams, and problem tricks. Click to open the drive link in a new tab.
📥 3D DOWNLOAD — Digital NotesUnderstanding current, current density, and potential together gives you the language to design, troubleshoot and explain real circuits. For example, in a PCB trace the designer must consider required current (I) and choose a trace width so that current density remains within safe limits. In power systems, transformers and cables are rated by allowable current and the associated heating; ignoring these leads to insulation failure.
When solving problems, always start with what is known: voltage sources, network connections, geometry of conductor (for current density), and whether steady-state or transient behavior is considered. Draw a quick sketch — mark current directions and potential references. Use sign conventions consistently; choose a reference (0 V) and stick to it.
Examples help: a 12 V battery connected to a lamp with 6 Ω resistance draws 2 A (V/R). If the conductor connecting the lamp is tiny (high current density), it will heat much more than a thicker wire — despite the same 2 A flowing. So current and current density together determine both performance and safety.
Example 1 — Simple calculation: A wire carries 5 A and has cross-sectional area 2 mm2 (2 × 10-6 m2). Current density J = I / A = 5 / (2e-6) = 2.5e6 A/m2. That number tells an engineer whether the conductor will overheat.
Example 2 — Potential hill: If two points differ by 9 V, a 1 C charge moving between them changes energy by 9 J. For tiny charges, scale accordingly — electrons have charge ~1.6e-19 C, so energy per electron is tiny in joules but significant at device scale.
- Label currents, polarities and reference nodes on a diagram.
- Use J = I/A to check heating risks for conductors.
- Use V = IR for simple circuits and energy = V × Q for work/energy checks.
- When in doubt, reduce current density (thicker wire) or split current across parallel paths.
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