Loaded pickup output

Into a real load, through the coil's own resistance and inductance, what comes out?

The formula

VL = \frac{ε \cdot RL}{\sqrt{{(Rc + RL)}^{2} + {(ω \cdot Lc)}^{2}}}

LaTeX

VL = \frac{ε \cdot RL}{\sqrt{\left(Rc + RL\right)^{2} + \left(ω \cdot Lc\right)^{2}}}

Work it out

ε Open-circuit peak EMF

The pickup-EMF page's peak, before anything loads it.

Rc Coil resistance

The pickup winding's DC resistance — the coil-from-gauge page's figure.

Lc Coil inductance

The pickup winding's inductance.

RL Load resistance

What the coil is connected to. An oscilloscope is a megohm; a lamp is a few ohms.

te Pulse width

The edge crossing time — the width of each half of the bipolar pulse.

f Slug rate

Slugs passing the coil per second — the drive's pulse repetition rate. Each slug gives two pulses.

or see a worked example with typical numbers

Each half of the bipolar pulse is taken as a half-sine of width t_e, which is a sine at frequency 1/(2 t_e): the effective angular frequency is ω = π/t_e.
The coil's impedance at that frequency is R_c in series with jωL_c; the load voltage is the EMF times R_L over the magnitude of the whole loop's impedance, √((R_c + R_L)² + (ωL_c)²). The load current is that voltage over R_L.
The mean-square of a half-sine is half its peak squared, so the power during a pulse is ½ V_L I_L. Two pulses of t_e per slug at f slugs per second is a duty of 2 t_e f, capped at 1; the mean power is the pulse power times the duty.
The load that draws the most power from a source with impedance Z is |Z| for a resistive load, so the matched load is √(R_c² + (ωL_c)²).

The half-sine stands in for the real pulse, which is nearer a trapezoid for a square edge through a finite coil and a smoother hump for a smeared one. The effective frequency is right to within a factor of about two, which matters only when ωL_c is comparable with the resistances — for the coils and speeds on the estate's figures it rarely is.
Linear, resistive load. A rectifier and reservoir capacitor is neither; its input looks like a much higher resistance until the capacitor charges and then like a short — the alternator-phases page gives the rectified mean for that case.
The coil's self-capacitance is left out. It matters when the pulse is short enough to approach the coil's self-resonance, which for a pickup of thousands of turns can be tens of kilohertz; at the millisecond pulses of a fluid slug it does not.
The load's power is the mean over pulses and gaps. A reader looking at the peak on a scope and multiplying by the peak current has the pulse power, which is 1/δ times larger and is not what a lamp or a battery sees.
Nothing here is Meyer's. The estate names no load for the pickup coils; the page exists because an open-circuit EMF says nothing about power until a load is put across it, and the archive's rule is that the arithmetic is shown.