My oscilloscope's inputs are rated "250V DC + AC peak (10 KHz)." Does this mean it would withstand mains voltage (325V peak) or only 250V DC? I have no plans on doing this any time soon, I am only curious.
if you add peak voltage to your dc offset, it must be less than 250V.
this was verified with dc and a 10kHz ac wave.
AC signals sometimes ride on a DC voltage level. On the scope you may see a sin wave of +60 to - 40 VDC. This is 100 V Ac signal riding on a 10 V DC voltage.
I once worked with a 10 V peak to peak sin and cos signal from a resolver. The reference signal had a 0 V, 400 mV or 800 mV DC level applied to it. A multiplexer would switch between 3 different resolvers based on DC level.
Your scope could handle anything from 250 V peak AC signal to a peak 125 VAC on top of 125 V DC to a pure 250 V DC or any mix as long as the AC Peak signal + the DC level is less then 250 V
For dealing with High voltage signals, use high voltage probes. These typically reduce the signal by a factor of 10 or more. So a 250 VAC signal become a 25 V signal.