Argh! This thread makes me cringe, and I fear for the OP's oscilloscope.
Some thoughts coming out of my cringe:
DougSpindler: Please please do watch Dave's video linked just above by rstofer. Watch it several times.
Why do people with little scope experience always seem to want to probe the mains, first thing? It seems this comes up with every new scope owner.
Differential probing is the only safe way to probe the mains, especially if the house mains outlet is accidentally miswired, as the post about the soldering iron powering a circuit may indicate. But you have to understand what you are doing before you try it, since you can easily damage the scope or even hurt yourself badly.
Please please do construct a simple 555- based signal generator. For under 5 dollars in parts you can build a basic generator that will produce sine, triangle, and square wave outputs simultaneously. You can learn a lot by building this circuit and then probing around in it with your new
toy precision test instrument.
See
http://8085projects.info/555-waveform-signal-generator-circuit.html for just one example.
The following is greatly simplified and I'm sure we will have more input on the topics I mention.
100 MHz bandwidth is not necessarily a limit on the "frequency" that the scope can display. It IS a limit on the ability to display fast transitions, so at higher and higher frequencies a true square wave input signal will tend to look more and more sinusoidal.
The 1x, 10x probe settings are not "multipliers", they are _divisors_. That is, when the probe is set to 10x, this means that, say, a true 10 volt signal will be read as 1 volt by the probe, and the corresponding scope channel must be set also to 10x to display this as the correct 10 volt level. Almost _all_ normal circuit testing should be done with the 10x setting as this will apply the least loading to the DUT, and it also helps to protect the scope input from inadvertent overloads. 99.999 percent of the time you will want your probe 1x/10x switch and channel settings to match. The Rigol and most other scopes default to 10x channel setting for a reason. Keep your probes set to 10x unless you have a special case for using 1x.
The Rigol DS1054z has Cat 1 inputs rated 300 VRMS. Does this mean you can measure a 3000 volt signal with a 10x probe? Better not try it -- you need a 100x probe with a rating higher than 3000V. My own 100x probe is only rated to 2000 V. But probes and inputs must be de-rated as to max voltage as the signal frequency goes up. See the Data Sheet for your probes, and look up the definition and limits of "Category 1" test gear.
With isolation transformer: Don't float the scope, float the DUT !! Also be aware that using, say, BNC patch cords to connect a floated scope to another instrument like a function generator this automatically connects the scope chassis ground to that other instrument, which may be normally grounded itself. SO if you float the scope but don't also float the FG, your floating is useless. Also many FGs have the BNC output shield (outer connector) connected to chassis ground and hence to mains ground, so you must be careful not to make groundloops when connecting scope and FG to a DUT. And remember that all probe "ground" reference leads are connected together at the scope chassis and thence to the mains cord ground connection. So if your DUT is floated with an isolation transformer, and the scope isn't, then connecting a probe reference lead to the DUT will make that connection to mains ground back through the probe, scope and line cord.