CT sensors - An introduction
Often referred to as a current clamp, the CT is in fact, not a clamp.
These are Current Clamps:
Note the tensioning screws.
Pictured below, is an example of a Split-Core CT.
Current transformers (CTs) are sensors that measure alternating current. They are particularly useful for measuring whole building electricity consumption (or generation, for that matter).
The split core type, such as the CT in the picture above, is particularly suitable for DIY use, as it can be clipped onto either the live or neutral wire coming into the building, without the need to do any high voltage electrical work.
Like any other transformer, a current transformer has a primary winding, a magnetic core, and a secondary winding.
In the case of whole building monitoring, the primary winding is the live or neutral wire (not both!) coming into the building, that is passed through the opening in the CT. The secondary winding is made of many turns of fine wire housed within the transformer case.
The alternating current flowing in the primary produces a magnetic field in the core, which induces a current in the secondary winding circuit .
The current in the secondary winding is proportional to the current flowing in the primary winding:
Isecondary = CTturnsRatio x Iprimary CTturnsRatio = Turnsprimary / Turnssecondary
The number of secondary turns in the CT pictured above, is 2000, so the current in the secondary is one 2000th of the current in the primary.
Normally, this ratio is written in terms of currents e.g. 100:5 (for a 5A meter, scaled 0 - 100A). The ratio for the CT above would normally be written as 100:0.05.
A "current output" CT needs to be used with a burden resistor. The burden resistor completes or closes, the CT secondary circuit. The burden value is chosen to provide a voltage proportional to the secondary current. The burden value needs to be low enough to prevent CT core saturation.
The secondary circuit is galvanically isolated  from the primary circuit. (i.e. it has no metallic contact)
A CT is potentially dangerous if open-circuited.
References and further reading