Interactive Tools

Frequency and Wavelength

Frequency in hertz Display amplitude

Show step-by-step relation

The tool keeps Steinmetz’s spectrum relation in view: velocity equals frequency times wavelength. If the propagation velocity is fixed, raising frequency shortens wavelength in the same proportion.

AC Waveform And Harmonics

Fundamental amplitude Third harmonic percent Fifth harmonic percent Phase shift

This tool is keyed to Steinmetz’s repeated concern with alternating wave shape, higher harmonics, RMS/effective value, and the difference between ideal sine-wave theory and practical electrical waves.

$$e(t) = E_1\sin(\omega t + \theta) + E_3\sin(3\omega t) + E_5\sin(5\omega t)$$

Impedance and Reactance

Resistance R Reactance X

Phasor And Symbolic Form

Magnitude Phase angle Wave cycles

This tool follows Steinmetz’s symbolic-method sequence: a sine wave can be represented by a vector, the vector can be resolved into rectangular components, and the quadrature component can be marked with j.

$$A = a + jb$$ $$a = A \cos \theta,\qquad b = A \sin \theta$$

Power Factor

RMS voltage RMS current Phase angle in degrees

Hysteresis Loop And Steinmetz Loss

Maximum magnetic density B Frequency Hysteresis coefficient eta Steinmetz exponent Loop lag

This tool is a coefficient-based working calculator for Steinmetz’s hysteresis-loss relation. The exact historical units and typography still require scan verification, so the calculator keeps eta as a tunable coefficient rather than pretending that one modern unit convention has already been finalized.

$$W = \eta B^n$$ $$P = f\eta B^n$$

The classic exponent is kept adjustable, with n = 1.6 as the historically important starting point.

Transient RLC Response

Resistance R Inductance L in millihenrys Capacity C in microfarads Initial condenser volts

This tool is keyed to Steinmetz’s condenser charge and discharge discussion in Theory and Calculation of Transient Electric Phenomena and Oscillations. It uses the modern series-RLC form as a mathematical translation of the source equations for oscillating discharge, critical resistance, and decrement.

$$f = \frac{1}{2\pi}\sqrt{\frac{1}{LC} - \left(\frac{r}{2L}\right)^2}$$ $$r_1^2 = \frac{4L}{C}$$

Use it with the original figure pages and equation page rather than as a replacement for them: original transient figures and condenser oscillation frequency and decrement.

Lightning And Surge Traveling Wave

Surge amplitude Line length in km Velocity fraction of light Load impedance ratio Time after launch

This tool uses a modern transmission-line reflection model as a reading aid for Steinmetz’s transient-line and surge material. It is not a replacement for source extraction; it helps readers see why line length, propagation velocity, and terminal conditions matter.

$$\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$$

Tool Interpretation Rule

Every calculator on this page is a reading aid. It can clarify the mathematics, but it does not replace source-page verification, original notation, or the scan-linked equation pages.