This question is aimed to TRUE Elec Engineers, not fuse or wire directionality believers.

Interesting followup- I just tried the same experiment, but substituted a ClarityCap ESA, 33uF, 250V cap and got a constant 1.45VDC reading, with either polarity. 

@Rodman99999, I'm not sure how to explain those results, but if I understand correctly the meter was indicating the voltage across a series combination of the battery, the cap, and the tweeter.  Wouldn't it be more meaningful to put the meter across just the tweeter, and put the battery across the series combination of the cap and the tweeter?

Regards,
-- Al 

Same results, for a moment. BUT, now the tweeter’s blown(it literally/audibly, "popped"). Trying to read, across the tweeter’s terminals, wasn’t any more, "meaningful"(since I already knew DC voltage would pass), BUT- decidedly more EXPENSIVE! Explaining the results is easy(ie: non-polarized film capacitors, WILL pass DC).

ssg308,

Crydom relays are typically for motor control apps.  They will not have a low enuf switching resistance and linear frequency response for an audio signal.

Ouch!  Sorry to hear that, Rodman. 

I'm very surprised, though.  Here is a datasheet for an Energizer alkaline "C" battery, indicating a **minimum** nominal internal resistance of 0.15 ohms.  Even if we make the extremely unrealistic assumption that it could maintain an output of 1.5 volts into a direct short, and even if we make the extremely unrealistic assumption that the DC resistance of the tweeter is zero, and even if the capacitor offered zero resistance to the resulting current, the battery could only provide (1.5^2)/0.15 = 15 watts, which in that situation would all be dissipated in its internal resistance.  While datasheets I've seen over the years for various tweeters all show power handling capabilities of at least several tens of watts.

Regards,
-- Al