General concepts
Electrical principles visualised through animation and interaction: change the parameters with sliders and see the effect instantly. No isolated formulas — everything in a visual context.
Fundamental quantities & components
Intensity (current)
Current = the flow rate of electric charge through a conductor
Current I
8 A
1 A
1 C/s
I = Q / t
Electric current I = how much charge (electrons) passes per second through a conductor. I = Q/t; unit: Ampere (A); 1 A = 1 C/s. Increase I → the electrons flow faster.
Voltage
Voltage = the potential difference that “pushes” the current (like water pressure)
Voltage U
12 V
1 V
1 J/C
Voltage U = the electric potential difference between two points; it is the “pressure” that pushes the current (analogy: the difference in water height). Unit: Volt (V); 1 V = 1 J/C.
Resistance
It opposes the flow of current; at a fixed voltage, a higher R → a lower current
Resistance R
6 Ω
I = U/R
2.00 A
U
12 V
R = U / I = ρ · L / S
Resistance R opposes the current. At a fixed U, I = U/R (double R → half the current). R = ρ·L/S (increases with length, decreases with cross-sectional area). Unit: Ohm (Ω). The current through R produces heat: P = I²·R.
Power
The energy consumed per second: P = U · I
Power P
60 W
P = U · I · 1 W = 1 V · 1 A
Power P = the energy consumed per second = the product of voltage and current (the area U×I). Unit: Watt (W). The bulb shines brighter when P increases.
Ohm’s law
Change the voltage and the resistance; the current flows faster or slower
Current I = U / R
2.00 A
Power P = U · I
24 W
I = U / R · P = U · I
The particles flow faster when the current is higher. At a lower R or a higher U → I increases.
The power triangle
How apparent power splits into active (P) and reactive (Q), as a function of cos φ
Active P
8.5 kW
Reactive Q
5.3 kVAr
Apparent power S
10 kVA
P = S · cos φ (kW, useful) · Q = S · sin φ (kVAr, reactive) · S = √(P² + Q²) (kVA). A lower cos φ → more useless reactive power.
Frequency & period
How many oscillations per second an alternating voltage makes
Frequency f
2 Hz
Period T = 1/f
0.50 s
Frequency (Hz) = the number of cycles per second; period T = 1/f. The grid in Romania: 50 Hz (T = 20 ms).
Inductance (Henry)
The coil opposes the change in current; the voltage is shifted +90°
U_L = L · di/dt · 1 H = 1 V·s/A
A coil stores energy in a magnetic field and opposes the change in current. In a.c., the voltage across the coil is shifted +90° ahead of the current. Inductance is measured in Henry (H).
Capacitance (Farad)
The capacitor charges and discharges exponentially (time constant τ = R·C)
τ = R · C
1.0
Charge
0 %
The capacitor stores charge: Q = C · U. It charges exponentially with the time constant τ = R · C (at 5τ it is ~99 % charged). Capacitance is measured in Farad (F).
Magnetic field
The circular field around a conductor carrying a current
The current generates a circular magnetic field around the conductor; the intensity increases with the current. The direction: the right-hand rule (thumb = the current, fingers = the field).
Alternating → direct current & measurement
Rectifier — AC → DC
Converting alternating current into direct current
Transformer (changes the amplitude according to the turns ratio) → rectifier bridge (4 diodes) → filter capacitor → direct voltage.
The transformer changes the voltage according to the turns ratio: U_secondary = U_primary / n. The bridge (4 diodes) flips the negative half-cycles; the capacitor “fills” the gaps (filtering). A larger capacitor → less ripple.
Voltmeter & Ammeter
How you connect them correctly — and what happens when you get it wrong
What you measure
Connection
✓ Correct. The voltmeter is connected in PARALLEL with the load; the ammeter in SERIES.
Voltmeter = high resistance, in PARALLEL (measures the voltage at the terminals). Ammeter = low resistance, in SERIES (the current flows through it). Swapping them is the classic mistake.
Kirchhoff’s laws
Kirchhoff’s laws
How currents and voltages divide in series and in parallel
I (total)
0.40 A
U1 / U2
4.0 / 8.0 V
I (comun)
0.40 A
Voltage law (KVL): around a loop, U = U1 + U2. In series the current is the same, and the voltage divides in proportion to R.
In series: I common, U divides (U = U1 + U2 — KVL). In parallel: U common, I divides (I = I1 + I2 — KCL).
Sources in series & in parallel
How the voltage and the current change when you connect several sources
Total voltage
24 V
In series (+ to −): the voltages ADD UP → U = U1 + U2. The available current stays the same. (E.g.: two 1.5 V batteries in series = 3 V.)
Series = the voltages add up (current unchanged). Parallel = the voltage stays the same, but the maximum current / runtime increases. In parallel the sources must have the same voltage (otherwise equalising currents appear).
Three-phase system
Three-phase sine waves
The three phases at 120° and the neutral current when you unbalance them
Balanced — the neutral current ≈ 0 (the three cancel vectorially).
At equal amplitudes, the sum of the three sine waves 120° out of phase is zero → the neutral is not loaded. See the “Three-phase balancing” page for the calculation.
Three-phase phasors (120° phase shift)
The three voltages as rotating vectors, 120° apart — a symmetrical system
Symmetric system (120° / 240° shifts) — the vector sum of the three ≈ 0 (they cancel out).
Vector sum (resultant)
0 V
resultant = U_phase × |R⃗ + S⃗ + T⃗| · U_phase = 230 V · symmetric (120°) → 0
The three phases R/S/T are vectors (phasors) of equal length, shifted by 120°. Move the S/T shift and watch their vector sum (resultant) grow from zero. It is a demonstration of the cancellation at 120°: in a real network the shift is fixed at 120°, and the neutral current arises from unequal loads on the phases (see the „Three-phase balance" page), not from changing the angle.
Star (Y) — Delta (Δ)
The two ways of connecting a three-phase system
Three-phase load — 3 windings (e.g. motor)
Phase voltage (L–N)
230 V
Line voltage (L–L)
400 V
Winding voltage
230 V
Only the winding voltage differs: star = 230 V · delta = 400 V
Star (Y): each winding is connected between a phase and neutral → it sees the phase voltage = 230 V (= U_line / √3). Line current = winding current.
The network voltages are fixed and standard: 230 V between phase and neutral, 400 V between phases (U_line = √3 × U_phase). What changes with star/delta is NOT these voltages, but how much voltage reaches each winding: in star 230 V (phase–neutral), in delta 400 V (phase–phase). That is why STAR-DELTA starting: you start in star (the winding gets only 230 V → reduced inrush current), then switch to delta for full power.
Protections
MCB curves — B / C / D
Where a circuit breaker trips: thermal (overload) or magnetic (short circuit)
Tripping curve
Below 1.13 × In it does not trip. Between 1.13 × In and the curve threshold → thermal (slow). Above the curve threshold (B 3× · C 5× · D 10× In) → magnetic (instant).
RCD / toroid — residual current
How an RCD “senses” a current leakage to earth
Tripping threshold: 30 mA
✓ Below threshold — does not trip
In normal operation, the current entering on the phase (L) = the current leaving on the neutral (N) → the sum in the toroid = 0. A leakage to earth (a touch, an insulation fault) diverts part of the current → I_L > I_N; the difference (the residual current) is detected by the toroid. At ≥ 30 mA the RCD trips (Art. 4.1.5.2.1).
Discussion
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