Deducing upper and lower bounds on resistance from a voltage and current waveform
Here is a math trick that you might find useful while looking at waveforms.
Imagine a tech printed and brought you a waveform that looks like this:
Blue trace is the voltage across leads of a solenoid, and the other one is the current. And, of course, there are no cursors on the waveform!
The tech asks -- is this good or bad? You ask the tech to look up the resistance spec for the solenoid. Ten seconds later the tech tells you -- 8-11 Ohms. You immediately say: "Not good". How did you do it?
Well, first you look at the current ramp and notice the point when the current stabilizes. At this point the current is limited only by DC resistance of the solenoid and Ohm's law is applicable in its traditional form: R = V / I. But, what are V and I, exactly? Should you try to figure that out using a ruler or send the tech back to redo the capture with cursors?
So, here comes the trick. You see that voltage V is between 14 and 15 Volts. The current is between 3 and 4 Amps.
If you take the higher voltage value and lower amperage value, you'll get the upper bound on resistance: R < 15 /3 = 5 Ohm.
If you take the lower voltage value and higher amperage value, you'll get the lower bound on resistance: R > 14 / 4 = 7 /2 = 3.5 Ohm.
So, the deduced range for the value of R is 3.5 - 5 Ohm, no cursors needed, and, if numbers are convenient, not even a calculator! Once the tech tells you the specs and they are significantly outside the deduced range, you know something is not right.
There are variables to this calculation. You need to make sure the measured voltage is the actual voltage across the solenoid and does not include, for example, normal voltage drop across the power transistor. The amp-clamp should be properly calibrated and be precise enough. To match the spec value, the solenoid should not be very hot at the beginning of the test. When the deduced and spec ranges overlap, no definitive conclusions can be made. But when the approach works and the resistances are clearly different, it's pretty neat.
There are extensions of this approach to other components such as resistive loads controlled by PWM. If you liked this trick and would like to learn more bounding tricks, please let me know.