How is a Kibble balance used in the new definition of the kilogram, and what's the connection between the balance and Planck's constant? [duplicate]

The BBC News article Kilogram gets a new definition says:

How does the new system work?

Electromagnets generate a force. Scrap-yards use them on cranes to lift and move large metal objects, such as old cars. The pull of the electromagnet, the force it exerts, is directly related to the amount of electrical current going through its coils. There is, therefore, a direct relationship between electricity and weight.

So, in principle, scientists can define a kilogram, or any other weight, in terms of the amount of electricity needed to counteract the weight (gravitational force acting on a mass).

Here's the tricky part

There is a quantity that relates weight to electrical current, called Planck's constant - named after the German physicist Max Planck and denoted by the symbol h.

But h is an incredibly small number and to measure it, the research scientist Dr Bryan Kibble built a super-accurate set of scales. The Kibble balance, as it has become known, has an electromagnet that pulls down on one side of the scales and a weight - say, a kilogram - on the other.

The electrical current going through the electromagnet is increased until the two sides are perfectly balanced.

By measuring the current running through the electromagnet to incredible precision, the researchers are able to calculate h to an accuracy of 0.000001%.

This breakthrough has paved the way for Le Grand K to be deposed by "die kleine h".

I don't understand the importance of Planck's constant to the use of the Kibble balance in new definition of the kilogram, and the way a Kibble balance is portrayed in the article suggests a kilogram-force rather than a kilogram, since the product $$GM_{Earth}$$ would be needed in the relationship between the force of the electromagnet on one side of the balance, and the gravitational force on the kilogram mass on the other.

I'm assuming that the left side measures the force of one winding upon another in series, rather than a slug of permeable iron.

This answer touches on this topic but here a more specific answer about the balance itself will be appreciated.

This answer mentions that local acceleration is indeed part of the measurement and can be addressed to a high degree of precision(?) However it doesn't explain how. Here I'm looking for an answer that gives a practical explanation how this will be done, rather than just being convinced that it could be done in principle.

marked as duplicate by Emilio Pisanty, user191954, uhoh, Rob Jeffries, David HammenNov 17 '18 at 11:15

• No worries. $\$ – Emilio Pisanty Nov 17 '18 at 8:47