Kibbla

Kibbla, a gold balance-paladin of The SI Guard, holds the beam of a Kibble balance level and weighs the kilogram with electricity.

The Physics

A Kibble balance runs in two modes. In weighing mode, a current I in a coil sitting in a radial magnetic field pushes up with force BLI, balancing the weight mg. In moving mode, the same coil is moved at speed v and a voltage U = BLv is induced. The hard-to-measure product BL cancels between the two, leaving a match between mechanical and electrical power.

mgv = UI

• m: test mass (kg)
• g: local gravitational acceleration (m/s²)
• v: coil velocity (m/s)
• U: induced voltage (V)
• I: coil current (A)

U and I are measured with the Josephson and quantum Hall effects, whose constants are K_J = 2e/h and R_K = h/e². Since 20 May 2019 the SI fixes h = 6.626 070 15 × 10⁻³⁴ J s exactly (with e also exact), so the balance turns the fixed value of h into a mass. The platinum-iridium prototype Le Grand K is no longer the definition.

Honest caveat: The equation is “virtual power”. The two modes run at different times, so no power actually flows; mgv = UI is a comparison, not an energy transfer. g and v must also be measured, with an absolute gravimeter and laser interferometry.

On the sticker

Kibbla holds the polished 1 kg mass in one hand and the glowing coil in the other. Printed text: KIBBLA with the line mgv = UI. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.