No, if the UL Rated Listing for the Panel is 200A than that's it. You cannot have 300A flowing through a 200A Panel.
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No, you cannot add 100 amps to a 200-amp rated electrical box. The box is designed to handle up to 200 amps safely. Exceeding this limit can lead to overheating, electrical fires, and other safety hazards. If you need more amperage, you would need to upgrade to a larger capacity electrical panel.
A #16 copper conductor is not a wiring size that is used in homes. This is because the smallest breaker for residential use is rated for 15 amps. A #16 copper conductor is only rated at 13 amps. For a load of 13 amps over 100 feet a #12 copper would be required.
I am assuming by your description that the panel is protected by a 90 amp breaker and the breakers in the panel when added up is 200. This is okay as long as your 90 amp breaker trips on a regular basis. It is typical for the breakers to add up to more than the main breaker under the assumption that you would rarely be running each circuit at its maximum capacity.
Add 25% so it comes to 42 amps
To determine the amp service in your house, locate the main electrical panel. The amp rating is typically labeled on the main circuit breaker. Common residential amp services are 100 amps, 150 amps, or 200 amps.
To convert VA (volt-amps) to amps, you need to know the voltage. If the voltage is 120V, then 150 VA is equivalent to 1.25 amps (150 VA / 120V = 1.25 A). If the voltage is different, you will need to adjust the calculation accordingly.