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# Assertion(A): Both DC and AC can be measured by a hot wire instrument.Reason(R): The hot wire instrument is based on the principle of the magnetic effect of current.A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.C. The assertion is correct but Reason is incorrect.D. Both Assertion and Reason are incorrect.

Last updated date: 18th Jun 2024
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Hint: Hotwire instrument is based on the heat $I_{rms}^2Rt$ and/or power $I_{rms}^2R$ (where ${I_{rms}}$ is the root mean square current, $R$ is resistance and $t$ is time) producing property of current. Hence it can measure both ac and dc current as both produce heat when passed through a conductor.
A hotwire instrument is not based on the principle of the magnetic effect of current.

Complete step by step solution:
First, we have to calculate the equivalent EMF and total equivalent resistance for the type of Let us first discuss the Assertion which states that “Both DC and AC can be measured by a hot wire instrument.”
A hot wire instrument is an electrical measuring instrument (basically an ammeter) in which the current to be measured is passed through a thin wire and causes its temperature to rise. The temperature rise, which is proportional to the square of the current, is measured by the expansion of the wire. Such instruments can be used for either direct current or alternating current.
Or in other words, we can say that the Hotwire instrument is based on the heat $I_{rms}^2Rt$ and/or power $I_{rms}^2R$ (where ${I_{rms}}$ is the root mean square current, $R$ is resistance and $t$ is time) producing property of current. Hence it can measure both ac and dc current as both produce heat when passed through a conductor.
So, the Assertion is correct.
Now discuss the Reason which states that “The hot wire instrument is based on the principle of the magnetic effect of current.”
A hot wire instrument works on the principle that the length of the wire increases because of the heating effect of the current flow through it.
Now, we can say that a hotwire instrument is not based on the principle of the magnetic effect of current.
So, Reason is incorrect.

$\therefore$ The Assertion is correct but the Reason is wrong. Hence, option (C) is the correct answer.

Note:
Construction of a hot wire instrument: The current whose magnitude is used to be determined is passed through the platinum-iridium wire. The hot wire instrument uses two-wire.
When the current passes through the platinum-iridium wire, it gets heated and expands. The heat increases the sag of the wire. The wire regains its original position with the help of the spring. The expansion and contraction of the thread rotate the pulley due to which the pointer deflects. The expansion of the thread is equal to the square of the RMS value of the current.