Science Lab: RLC, FFT, Chemistry & Psychrometrics

The Science Lab packs ten panels under one tab bar: RLC impedance, a Smith chart, signal FFT, error propagation, equation balancing, molar mass, an engineering handbook, psychrometrics, solution chemistry and dimensional analysis. Every panel has its own URL (/science/scilab/rlc, /science/scilab/fft, /science/scilab/psychro), so a bench can be linked or bookmarked; all of it computes in the browser.

Updated 2026-10-01Reviewed by CalcX Editorial Team5 sources5 min read

How to work a panel

Pick a panelfrom the tab bar, or open its URL directly. Electronics, chemistry and thermodynamics sit side by side, so read the panel name before trusting a number.
Enter values in the unit printed next to each field.RLC takes R in Ω, L in mH, C in µF and f in Hz; psychrometrics takes kPa and °C; the gas-law tab takes L. A component set to 0 is dropped from the network rather than treated as a zero-valued part.
Read the cards and reuse the result.Resonance cards (f₀, Q, bandwidth) appear only when both L and C are positive; the FFT prints Δf and its length above the plot, then up to six peaks. Panels can send values onward — the FFT offers the signal, spectrum or peak table, and molar mass exports CSV or Markdown.

Worked examples

Every readout below comes from the live panels; the same inputs reproduce them.

Panel · input	Readout
RLC Impedance · series: R 10 Ω, L 1 mH, C 1 µF, f 5033 Hz	Z 10 + j0.000990091 Ω; f₀ 5.0329 kHz; Q 3.1623; bandwidth 1.5915 kHz
RLC Impedance · parallel: same components	Q 0.31623; bandwidth 15.915 kHz; ∠Z -0.00056728°
Smith Chart: load 100 + j50 Ω, Z₀ 50 Ω	Γ 0.44721 ∠ 26.565°; VSWR 2.618; return loss 6.9897 dB; mismatch loss 0.9691 dB
Signal FFT: tones `50:1, 300:0.5`, N 1024, fs 2048 Hz	Δf 2 Hz; peaks 50 Hz · 1 and 300 Hz · 0.5
Error propagation: f = 4π²L/T², L 1.000 ± 0.001, T 2.006 ± 0.002	9.81065 ± 0.0219; relative 0.2231%; T contributes 79.9%, L 20.1%
Balance Equations: `KMnO4 + HCl -> KCl + MnCl2 + H2O + Cl2`	2KMnO4 + 16HCl → 2KCl + 2MnCl2 + 8H2O + 5Cl2
Molar Mass: CuSO4·5H2O	249.677 g/mol (O 57.67%, Cu 25.45%, S 12.84%, H 4.037%)
Psychrometrics: 30 °C, 50% RH, 101.325 kPa	dew point 18.45 °C; wet-bulb 22.01 °C; w 13.28 g/kg; h 64.135 kJ/kg; boiling point 99.841 °C

One convention to watch: the RLC rows share f₀ but not Q — series Q is Z₀/R (3.1623) against parallel Q = R/Z₀ (0.31623); the error row is a pendulum experiment (g = 4π²L/T²) where timing owns 79.9% of the variance and the ruler 20.1%.

Assumptions and limits

Units stay per-field.: L is entered in mH and C in µF, f₀ and bandwidth are shown in kHz, pressures in kPa and gas volumes in L — 22.414 L/mol at 0 °C and 101.325 kPa. The panels never convert units for you.
Psychrometric properties move with pressure.: The default 30 °C/50% state has w 13.28 g/kg and h 64.135 kJ/kg at sea level; switch the pressure source to altitude, enter 2000 m, and the same air reads w 17.03 g/kg, h 73.714 kJ/kg and a boiling point of 93.362 °C. The comfort card is a simplified ASHRAE 55 check (no air speed, radiant temperature, clothing or metabolic rate).
What it doesn't do.: It is not a circuit simulator, a data-acquisition front end or a general CAS: transient and AC circuit work belongs to the Engineering Lab, trajectories and orbits to the Physics Sim, and typed expressions with precedence and angle modes to the scientific calculator.

The window decides what a peak means

A 50.5 Hz tone (fs 2048 Hz, N 1024, Δf = 2 Hz) exposes the page's sharpest trap. The peak card reads 50 Hz · 0.9603 with the default Hann window, 50 Hz · 0.8996 under Rect and 50 Hz · 1 under Flat-top — the reported frequency is the bin centre, not the tone, and the height depends on the window. Hann suppresses leakage, Flat-top is amplitude-accurate on and off the grid, and Rect is only exact for signals that repeat over the sampled window. Quote the window with the number.

Where it fits

Electronics bench

Check series and parallel resonance, read VSWR and return loss off the Smith chart, and decode a 1 kΩ ±5% resistor as brown · black · red · gold. The handbook encodes a 4.7 kΩ target as yellow · violet · red · gold and finds exact pairs such as 1.1 kΩ + 3.6 kΩ = 4.7 kΩ.

Chemistry and lab prep

Balance an equation with charge, including ionic species; get molar mass and mass shares for a formula like CuSO4·5H2O; dilute 2 M stock to 0.5 M in 200 mL by adding 150 mL; build a 1:10 serial dilution; read pH 2.8753 for 0.1 M acetic acid and a weak-acid titration whose equivalence point is 50 mL at pH 8.722.

Measurement and data

Spectrum a sampled signal, propagate uncertainties and see which input dominates the variance, then check the working with dimensional analysis: F = m·a is consistent (M·L·T⁻² = kg·m/s²), 5 m/s * 3 s reads 15 m, and pipe-flow variables reduce to the group Π₁ = ρ·v·D/μ.

References

JCGM, JCGM 100:2008 — Evaluation of measurement data: Guide to the expression of uncertainty in measurement, bipm.org （访问日期：2026-10-01）— first-order variance composition for the error-propagation panel.
F. J. Harris, On the use of windows for harmonic analysis with the discrete Fourier transform, Proceedings of the IEEE 66(1), 1978, doi.org （访问日期：2026-10-01）— leakage and window amplitude trade-offs behind the FFT panel.
ASHRAE, Handbook — Fundamentals, Psychrometrics, ashrae.org （访问日期：2026-10-01）— humidity ratio, enthalpy and wet-bulb relations.
O. A. Alduchov and R. E. Eskridge, Improved Magnus form approximation of saturation vapor pressure, Journal of Applied Meteorology 35(4), 1996, journals.ametsoc.org （访问日期：2026-10-01）— saturation vapour pressure and dew point.
NIST, CODATA Recommended Values of the Fundamental Physical Constants, physics.nist.gov （访问日期：2026-10-01）— gas constant and Faraday constant used by the solution panels.