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iwire:
My goal is to try to help you understand how the circuit works.
A relay coil has both inductance and resistance that can be represented by a schematic series circuit of a pure (ideal) inductor and resistor. These two components in series are what you see looking at the relay coil terminals. In the real world these two elements are not separable. Thus, I can not put a scope across the resistive component of the coil, but I can measure the input current to the coil and from that deduce the voltage drop across the internal resistance vs time.
I can determine the value of the coil's internal resistance by a DC resistance measurement by waiting long enough for any transient affect to die out. For a typical small relay that is probably less than one second. Using appropriate instrumentation I can measure the coil's inductance independent of the coil's DC or AC resistance. An LRC bridge is that type of instrument. The LRC bridge with AC excitation can also be used to measure the inductance.
For a DC relay there are pull-in and drop-out voltages and currents. For one sample of a P&B KUP 11D15 24 VDC relay some measured values are:
1. 480 ohms DC coil resistance using a Fluke 27.
2. 476 ohms DC coil resistance using a General Radio 1650-A bridge.
3. 0.950 Henrys Q = 1.6 armature open at 1 kHz inductance using GR 1650.
4. 1.050 Henrys Q = 1.4 armature hand held closed with same instrument.
More later I have to leave.
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Gar, I know how the circuit works enough to wire and troubleshoot it.
I have no clue at all what a Henry is and no need to know the resistance of the coil.