If your main breaker is open and the utility meter is still measuring current, you probably have another circuit tapped ahead of the main. Usually there will be some sort of junction box with a breaker or fuse in it that is located close to the main panel and probably connected to the main panel with conduit. If you do not see a junction box in close proximity to the main panel then carefully remove the front cover of the main panel and look for a couple smaller wires that are tightened into the cable side of the main breaker. Either that, or check for a few wires that run out of the panel through the same conduit that runs to the meter. Those would be the two most likely terminations used by somebody (previous owner) trying to add a circuit to a full panel. If you can locate that tap, you should be able to follow the wire to determine what the load is. Although I've never heard of a meter measuring current when there is no load on it, you will need to call the utility company if you cannot find a circuit tapped ahead of the main breaker. They own the meter.
You would not be the first person to have someone else tap into your electric power. If you are in a detached house, it is fairly easy to find out. Turn off everything in the house. Leave the circuit breakers on. Have someone stand outside by the meter. See if the meter still runs. (You may need to turn off the breaker to the hot water.) If the meter is still running when nothing in the house is turned on, you can call the power company to come out and check.
Because the utility customer is providing energy to the grid. Usually because of net metering of renewable systems.
You do not remove the electric meter from a house. Ever. You could be electrocuted or have an explosion in front of your face, putting molten metal through you. You must call the power company and they will send a properly trained and properly safety-equipped technician to remove the meter from the house. Even the fire department is no longer authorized to "pull a meter". They would rather have your house burn down than risk the life of a firefighter making an attempt to pull the meter, even with firefighting protective equipment. Do not attempt to remove an electric meter from a house.
In BC, Canada it's the same way as a house, and I guess would be the same anywhere. - The electric company places a meter on a pole outside the house and the homeowner gets a qualified electrician to connect wiring from meter to power panel in home.
A voltmeter or a multi-meter.
If there is an electric short, the resistance of the circuit would be zero. So you can use an ohm meter to test it.
You measure a house fly in millimeters
I believe it would get cold..
In most houses you would.
Anything apart from unplugging/shutting off all the appliances would be considered fraud.
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You will have to run wires from your electric box in your house, I would suggest barring these wires.