Which instrument has a necessarily the “square law” type scale?

Which instrument has a necessarily the "square law" type scale?

SOLUTION

Hotwire instruments have a necessarily the “square law” type scale.

Working Of Hot Wire Instrument

The working of the hot-wire instrument is based on the heating effect of electric currents. When the current to be measured passes through the hot wire, the wire gets heated and then expands. Since the wire is fixed between two points, it sags due to expansion which is magnified by the phosphor-bronze wire and silk thread. This expansion is taken up by the spring and the silk thread, which causes the pulley to rotate, and the pointer is deflected.

Deflecting Torque

The deflection of the pointer of the hot-wire instrument is proportional to the extension of the hot wire, which is itself proportional to the square of the current.

Hence

Deflecting Torque. Td ∝ I2

If spring control is used, then

Controlling torque T∝ θ (deflection)

For balanced condition

TC = Td

θ ∝ I2

Thus, these instruments have a square-law type scale. They read the R.M.S value of current and are independent of its frequency.

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