## Teaser 2954: Lovely meter, RITA made!

**From The Sunday Times, 5th May 2019** [link]

Revisiting the old curiosity shop, I bought an unusual moving-iron ammeter (made by Rho Iota Tau Associates). On the non-linear scale “9” was the last possible “whole amperes” scale graduation marked before the “full scale deflection” end stop (which was a half turn of the pointer from zero).

The booklet gave the pointer swing from zero (in degrees) equal to the current (in amperes) raised to a fixed single-figure positive whole number power, then divided by a positive whole number constant. Curiously, the angle between “exact” pointer swings, calculated using this formula, for two single-figure “whole amperes” values was exactly a right angle.

What, in amperes, were these two currents (lower first) and to what power were they raised?

[teaser2954]

## Jim Randell 5:44 pm

on2 May 2019 Permalink |The title of the puzzle, of course, is a reference the song

Lovely RitabyThe Beatles.This Python program runs in 82ms.

Run:[ @repl.it ]Solution:The two currents are 3 A and 9 A. They are raised to the power of 8.So the formula for the deflection (in degrees) as a function of the current (in amps) is:

Giving the corresponding readings for currents from 0 to 10 amps:

So if you want to read small currents you had better be good at measuring very small angles.

There are two further solutions for single digit powers and single digit currents that give a difference of exactly 90°.

These are:

But these are disallowed by the condition that 9A should be on the scale and 10A off the scale. In the first case both 9A and 10A are on the scale, in the second case they are both off the scale. But they would be solutions to similar puzzles where the scale goes to 10A (but not 11A), or 8A (but not 9A), respectively.

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