Electrical Fundamentals
Part of Basic Electrical Circuits
The core concepts of voltage, current, resistance, and power that underlie all electrical work.
Why This Matters
Every person working with electrical systems—whether wiring a lamp, charging a battery, or building a generator—is working with four fundamental quantities: voltage, current, resistance, and power. These quantities are not abstract; they have direct physical meaning and precise mathematical relationships.
Without a clear grasp of these fundamentals, electrical work is guesswork. Why does the wire get hot? Because too much current is flowing through too little conductor. Why doesn’t the motor start? Because voltage is dropping too much along the supply wire. Why did the battery drain so fast? Because the load demanded more current than calculated. Every one of these questions has a precise answer rooted in fundamental electrical principles.
This knowledge was formalized in the 19th century but the physics was available earlier. A rebuilding community that masters these fundamentals can design electrical systems correctly from first principles, rather than copying circuits without understanding why they work.
Voltage: Electrical Pressure
Voltage (V, measured in volts) is the difference in electrical potential between two points. It is analogous to water pressure: just as pressure drives water through a pipe, voltage drives current through a conductor.
Voltage is always a difference between two points. “12 volts” means 12 volts higher than the reference point (usually called ground or common). A point cannot have a voltage in isolation—voltage is always relative.
Sources of voltage:
- Chemical reaction: Batteries convert chemical energy to electrical potential
- Electromagnetic induction: Generators convert mechanical motion to voltage via magnetic fields
- Thermoelectric effect: Temperature difference across dissimilar metals creates a small voltage (thermocouples)
- Photoelectric effect: Light striking certain materials releases electrons (photovoltaic cells)
- Piezoelectric effect: Mechanical stress on certain crystals generates voltage
Measuring voltage: A voltmeter connects in parallel across the two points being measured. It must have very high internal resistance so that it draws negligible current and does not disturb the circuit.
A galvanometer with a large series resistor makes a voltmeter. If the galvanometer full-scale deflection current is 1 mA and you want full scale to read 10V, add a series resistor of 10V / 0.001A = 10,000Ω.
Current: Electron Flow
Current (I, measured in amperes or amps) is the rate of charge flow past a point. One ampere equals one coulomb of charge (6.24 × 10¹⁸ electrons) passing per second.
Current flows from the positive terminal of a source, through the external circuit, and back to the negative terminal. This is called conventional current direction (historically established before the electron was discovered). Electrons actually move in the opposite direction—from negative to positive—but for circuit analysis, the conventional direction gives correct results.
Measuring current: An ammeter connects in series—it must be in the path of the current it measures. Ammeters have very low internal resistance to minimize voltage drop.
A galvanometer with a small parallel (shunt) resistor makes an ammeter. The shunt carries most of the current while the galvanometer measures a small fraction. If galvanometer full-scale is 1 mA and you want to measure up to 1A, the shunt must carry 999 mA while the galvanometer carries 1 mA. Shunt resistance = (1 mA / 999 mA) × R_galvanometer.
Direct current (DC): Flows in one direction only. Batteries produce DC.
Alternating current (AC): Flows back and forth, reversing direction at a fixed frequency. Generators produce AC naturally. Household current is typically AC at 50 or 60 Hz.
Resistance: Opposition to Flow
Resistance (R, measured in ohms, Ω) is a material’s opposition to current flow. It converts electrical energy to heat.
Resistance depends on:
- Material: Copper has low resistance; rubber has extremely high resistance
- Length: Longer = higher resistance (proportional)
- Cross-section: Thicker = lower resistance (inversely proportional)
- Temperature: Most metals increase in resistance as temperature rises
Formula: R = ρ × L / A
Where ρ is resistivity (a material property), L is length, and A is cross-sectional area.
Conductance is the inverse of resistance (G = 1/R), measured in Siemens (S). High conductance means low resistance—the conductor passes current easily.
Ohm’s Law: The Core Relationship
Georg Ohm discovered in 1827 that for many materials, the ratio of voltage to current is constant (at constant temperature). This constant ratio is resistance.
Ohm’s Law: V = I × R
This single equation, rearranged three ways:
- V = I × R (find voltage given current and resistance)
- I = V / R (find current given voltage and resistance)
- R = V / I (find resistance given voltage and current)
Ohm’s Law triangle: Draw a triangle with V on top, I and R on the bottom. Cover the quantity you want to find; what remains shows the operation (side-by-side = multiply, stacked = divide).
Practical examples:
A 12V lamp draws 2A. What is its resistance? R = V/I = 12/2 = 6Ω
A circuit has a 100Ω resistor connected to a 9V battery. How much current flows? I = V/R = 9/100 = 0.09A = 90 mA
A 24V supply drives 3A through a wire. What is the wire resistance? R = V/I = 24/3 = 8Ω — this is excessive for a supply wire; indicates a thin or long conductor
Power: The Rate of Energy Use
Power (P, measured in watts, W) is the rate at which energy is consumed or delivered. One watt equals one joule per second.
Power formula: P = V × I
Combined with Ohm’s Law, power can be expressed three ways:
- P = V × I
- P = I² × R (current squared times resistance — the “heating effect” formula)
- P = V² / R
Energy is power over time: E = P × t (in watt-hours or joules)
A 60W lamp running for 5 hours consumes 300 watt-hours = 0.3 kilowatt-hours of energy.
Practical power calculations:
How long will a 12V/100Ah battery run a 25W load? Current draw = P/V = 25/12 = 2.08A Hours = 100Ah / 2.08A = 48 hours (theoretical; practical is about 60-70% of this)
A resistor carries 2A and has 6V across it. What power does it dissipate? P = V × I = 6 × 2 = 12W — this resistor needs to be rated for at least 12W or it will overheat
A pump motor runs from 24V and draws 5A. What is its power consumption? P = 24 × 5 = 120W
Energy Conversion Efficiency
No energy conversion is perfectly efficient. Electrical energy becomes heat, mechanical energy, light, and chemical energy. The efficiency is the ratio of useful output energy to total input energy.
Example: A motor converts 120W of electrical input into 90W of mechanical output. The remaining 30W becomes heat. Efficiency = 90/120 = 75%
Common efficiencies for rebuilt systems:
| Device | Typical efficiency |
|---|---|
| Copper wire (short run) | 98–99% |
| Copper wire (long run) | 85–95% |
| Simple transformer | 85–95% |
| DC motor | 60–85% |
| Lead-acid battery (charge/discharge) | 70–85% |
| Incandescent lamp | 2–5% (light) |
| Arc lamp | 8–12% (light) |
Maximizing efficiency reduces fuel consumption, heat generation, and battery drain. In resource-constrained rebuilding, every percentage point of efficiency matters.
Ground and Reference Points
Ground (or common) is the reference node in a circuit—the point defined as zero volts. All other voltages are measured relative to it.
In standalone systems, ground is simply a circuit node (usually the negative terminal of the power supply). In systems connected to buildings or equipment, ground is also the earth connection—a physical conductor driven into the soil that provides a return path for fault currents.
Safety grounding connects equipment chassis to earth. If a fault connects the live conductor to the chassis, current flows to earth through the ground connection rather than through a person touching the chassis.
Understanding ground is essential for both proper circuit analysis and for building safe electrical installations.