The deflection of a hot wire instrument depends on the RMS value of the A.C. current. Let's understand why this is the correct answer.



A hot wire instrument is an electrical measuring instrument used to measure the alternating current (A.C.) in a circuit. It consists of a thin wire that is heated by the current flowing through it. The wire expands due to heating, and this expansion causes a deflection of the wire. By measuring the deflection, the magnitude of the current can be determined.



The deflection in a hot wire instrument is primarily caused by the thermal expansion of the wire. When an A.C. current flows through the wire, it heats up the wire due to its resistance. The wire expands and contracts rapidly with each cycle of the alternating current.



The RMS (Root Mean Square) value of an A.C. current is a measure of the effective or average value of the current. It accounts for both the magnitude and the time variation of the current. The RMS value is calculated by taking the square root of the average of the squares of the instantaneous values of the current over a complete cycle.



The deflection of the hot wire instrument is directly related to the RMS value of the A.C. current. As the current increases, the wire heats up more, causing greater expansion and deflection. Similarly, as the current decreases, the wire cools down, causing less expansion and deflection.

Since the deflection is a measure of the current, it is essential to consider the RMS value rather than the average value of the A.C. current. The average value does not accurately represent the magnitude of the current, as it does not account for the varying nature of the A.C. waveform.

Therefore, the deflection of a hot wire instrument depends on the RMS value of the A.C. current rather than the average value of the A.C. current.