Assertion (A): A hot wire ammeter has a cramped scale Reason (R): The heat is proportional to the square of the current
Right Answer is:
Both A and R are true and R is the correct explanation of A
SOLUTION
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 Tc ∝ 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. Since the deflection of the pointer is proportional to the square of the current flowing through the coil. The scale of the instrument is, therefore. a cramped scale (NON-LINEAR) i.e. there will be congestion at the beginning of the scale.