Voltage, Current, Resistance and Power
🌐 Machine-translated page. The German version is authoritative.
The water circuit picture
Section titled “The water circuit picture”Imagine a water pipe with a pump. The pump creates pressure, the water flows, a narrow pipe slows the flow. In electrical engineering, these three things are called:
| Water | Electrical engineering | Symbol | Unit |
|---|---|---|---|
| Pressure | Spannung (voltage) | U | Volt (V) |
| Amount of water per second | Strom (current) | I | Ampere (A) |
| Narrowness of the pipe | Widerstand (resistance) | R | Ohm (Ω) |
The Spannung is the “drive”, the Strom is what actually flows, and the Widerstand is what limits it. Without Spannung there is no Strom. And none without a closed loop either: Strom only flows if it can travel from the source through the Verbraucher (load) and back to the source. That’s why every Steckdose (socket outlet) has at least two contacts: Außenleiter L (line conductor, “there”) and Neutralleiter N (neutral conductor, “back”).
Spannung U – the drive
Section titled “Spannung U – the drive”The Spannung is the difference in electrical “pressure” between two points. In Germany, the grid supplies 230 V between an Außenleiter and the Neutralleiter (alternating voltage, 50 Hz). Between two Außenleitern it is 400 V – more about that on the page Netz und Leiterfarben.
Remember: Spannung exists between two points. You measure it in parallel across the component, i.e. with the meter connected between the two terminals.
Typical values: AA battery 1,5 V · car battery 12 V · Steckdose 230 V · cooker/three-phase 400 V · medium-voltage grid 10–30 kV.
Strom I – what flows
Section titled “Strom I – what flows”The Stromstärke (current intensity) tells you how much charge flows through the conductor per second. 1 ampere is one coulomb per second – you don’t need to know that by heart, but you do need a feel for the orders of magnitude:
| Verbraucher (load) | Strom at 230 V |
|---|---|
| LED lamp 8 W | 0,035 A (35 mA) |
| Laptop power supply 65 W | 0,3 A |
| TV 100 W | 0,4 A |
| Vacuum cleaner 900 W | 3,9 A |
| Kettle 2 000 W | 8,7 A |
| Fan heater 2 000 W | 8,7 A |
| Socket circuit, LS B16 | max. 16 A |
You measure Strom in series – the meter is looped into the Stromkreis (circuit), or you use a Stromzange (clamp meter) around the conductor. An ammeter connected in parallel across 230 V is a Kurzschluss (short circuit).
Danger to humans: Just about 30 mA through the body can be deadly (ventricular fibrillation). That’s why RCD/FI-Schutzschalter (residual current devices) in homes trip at 30 mA of fault current – see Schutzorgane.
Widerstand R – what slows things down
Section titled “Widerstand R – what slows things down”Every conductor and every Verbraucher has a Widerstand. A long, thin wire has more Widerstand than a short, thick one. Copper conducts well, iron less well, plastic hardly at all (Isolator, insulator).
For cables, the following applies: the Widerstand grows with length and decreases with the Querschnitt (cross-section). That’s why a long supply cable gets a larger Querschnitt – otherwise Spannung is lost along the way (Spannungsfall, voltage drop) and the cable heats up.
Rule-of-thumb values for copper: 1,5 mm² ≈ 12 Ω per km · 2,5 mm² ≈ 7,4 Ω per km · 10 mm² ≈ 1,8 Ω per km (per core).
Ohm’s law
Section titled “Ohm’s law”The three quantities are related:
U = R · I – Spannung = Widerstand times Strom
Rearranged: I = U / R and R = U / I. This is the most important formula of your Ausbildung (apprenticeship). A triangle helps you remember it: U on top, R and I side by side below. Cover up the quantity you are looking for – what remains is the calculation.
Example 1: A fan heater has 26,5 Ω. At 230 V, I = 230 V / 26,5 Ω ≈ 8,7 A flows.
Example 2: A light bulb carries 0,26 A at 230 V. Its Widerstand is R = 230 V / 0,26 A ≈ 885 Ω (in the hot state).
Example 3: In a 12-V vehicle electrical system, 2 A flow through a lamp. R = 12 V / 2 A = 6 Ω.
Leistung P – how much work per second
Section titled “Leistung P – how much work per second”The Leistung (power) is Spannung times Strom:
P = U · I – Leistung in watt (W), 1 000 W = 1 kW
Combined with Ohm’s law: P = U² / R and P = I² · R.
Example: Kettle 2 000 W at 230 V: I = P / U = 2 000 W / 230 V ≈ 8,7 A. Two kettles on one power strip: 17,4 A – the LS B16 trips. That’s not a defect, that’s protection.
With alternating current and motors, the Leistungsfaktor cos φ (power factor) comes into play (Scheinleistung S in VA, Wirkleistung P in W). For resistive loads like heaters and light bulbs, cos φ = 1 – that’s enough for a start.
Energie W – Leistung times time
Section titled “Energie W – Leistung times time”The electricity meter doesn’t count Leistung, but Energie (energy):
W = P · t – Energie in kilowatt-hours (kWh)
Example: Fan heater 2 kW, 3 hours: W = 2 kW · 3 h = 6 kWh. At about 35 ct/kWh, that’s 2,10 €. An LED lamp with 8 W needs 750 hours for 6 kWh.
The units and their prefixes
Section titled “The units and their prefixes”| Prefix | Factor | Example |
|---|---|---|
| m (milli) | 0,001 | 30 mA tripping current of an RCD |
| k (kilo) | 1 000 | 2 kW kettle, 10 kV medium voltage |
| M (mega) | 1 000 000 | 1 MΩ minimum insulation resistance |
Always calculate in base units (V, A, Ω, W) and only convert at the end. Most calculation mistakes at Berufsschule (vocational school) are unit mistakes.
What you can do now
Section titled “What you can do now”- Distinguish between Spannung, Strom, Widerstand and Leistung and name their units.
- Use U = R · I and P = U · I to calculate any missing quantity.
- Understand why an LS-Schalter (miniature circuit breaker) trips when too many devices are running and why 30 mA is dangerous for the body.
Next up is the grid that all of this hangs on: Netz und Leiterfarben.
Test yourself
Section titled “Test yourself”🧠 Test yourself