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VOLT shows you the voltage, current and power on every part — but knowing the equations behind those numbers is what turns playing into understanding. Work a value out by hand, then check it against the board. If your math and the simulator agree, you've got it. If they don't, one of you is wrong — and finding out which is how you learn.
V = I × R → I = V / R → R = V / IVoltage (V, volts) = current (I, amps) × resistance (R, ohms). The single most useful equation in electronics.P = V × I = I²R = V²/RPower in watts — how fast energy is used (heat, light, motion). A part's wattage rating must beat this or it burns.R = R₁ + R₂ + R₃ …Resistances add up. The same current flows through every one.1/R = 1/R₁ + 1/R₂ … (two: R₁R₂ / (R₁+R₂))Total resistance DROPS below the smallest one. Each branch sees the same voltage.V out = V in × R₂ / (R₁ + R₂)Two resistors split a voltage. R₂ is the one you measure across. The heart of sensors, pots and references.R = (V supply − V led) / I lede.g. a red LED (≈2 V, 20 mA) on 9 V: (9−2)/0.02 = 350 Ω → use the next standard up, 360–470 Ω. Never wire an LED with no resistor — it burns out.sum to 0.Everything the battery pushes out is used up by the parts on the way back. Add the drops — they equal the supply.current in = current out.Charge doesn't pile up. What flows into a junction flows back out across its branches.Q = C × V · RC time constant: τ = R × CAfter one τ a capacitor is ~63% charged; ~5τ ≈ full. V(t) = V full × (1 − e^(−t/τ)). (VOLT's instant view is steady-state — the live charging curve is the transient scope.)τ = L / R · Reactance: X C = 1/(2πfC), X L = 2πfLReactance is "resistance" to AC: caps fight high frequencies less, inductors more.f = 1 / (2π√(LC))The frequency an L and C ring at together — the basis of every tuner, oscillator and filter.Q = I × t · 1 Ah = 3600 C · 1 C = 6.24 × 10¹⁸ electronsCurrent is charge per second. A 3000 mAh battery holds 10,800 coulombs.E = P × t · E = Q × V · 1 kWh = 3.6 MJWatts for seconds = joules. The bill is in kWh: a 1500 W heater for 1 h = 1.5 kWh.1 eV = 1.602 × 10⁻¹⁹ JThe energy one electron gains crossing 1 V. Just joules per electron — a 5 V supply gives each electron 5 eV.F = k × q₁q₂ / r², k = 8.99 × 10⁹ N·m²/C²Like charges push, opposite pull, and the force falls with the square of distance — the root of voltage, capacitance and static shocks.E C = ½ C V² · E L = ½ L I²A capacitor stores energy in its electric field, an inductor in its magnetic field. The ½ is because V (or I) rises while charging.Z = √(R² + (X L − X C)²) · φ = atan((X L − X C) / R)Resistance plus reactance, at right angles. φ is how far current lags (inductive) or leads (capacitive) the voltage.P = V I cos φ (W) · Q = V I sin φ (VAR) · S = V I (VA) · S² = P² + Q²Real power does work, reactive power sloshes back and forth, apparent power is what the wires and transformer must carry. pf = P / S = cos φ.P = √3 × V LL × I × pf · V LN = V LL / √3480 V line-to-line is 277 V line-to-neutral. The √3 is why three wires carry 1.73× the power of two.V rms = V peak / √2 (sine) · V peak = 1.414 × V rms120 V mains peaks at 170 V. RMS is the DC-equivalent heating value — what meters read.V p / V s = N p / N s · V p I p = V s I s · I = kVA × 1000 / V (1φ)Turns ratio sets the voltage; power in equals power out (minus losses), so stepping voltage down steps current up.ε = −N × dΦ/dtA changing magnetic flux through N turns induces a voltage that opposes the change. Every generator, transformer and inductor runs on this line.η = P out / P in · P loss = P in − P outA 10 HP motor at 91% draws 8.2 kW to deliver 7.46 kW; the 0.74 kW difference is heat.V th = V s × R₂ / (R₁ + R₂) · R th = R₁ ∥ R₂ · P max at R L = R thAny linear network looks like one source and one resistor from the outside. A load equal to R th pulls the most power — and only half the efficiency.P = I² R · R = ρ L / A · R T = R₂₀ × (1 + 0.00393 (T − 20)) (copper)Long thin wires get hot. Copper's resistance rises ~0.4% per °C — a 75 °C conductor is 22% more resistive than at room temperature.dB = 10 log₁₀(P₂/P₁) = 20 log₁₀(V₂/V₁) · dBm = 10 log₁₀(P / 1 mW)+3 dB doubles power, +10 dB is 10×, −3 dB is the half-power (0.707 V) point every filter is rated at.Every quick question from the first resistor to a 480 V feeder, a solar string or an arc-flash label. Pick a group, tap a tool, star the ones you use.
Hold the resistor so the tolerance band (gold / silver, or the lone band sitting farther from the others) is on the right. Then tap the colors left-to-right. The value updates as you go.