Question

What is meant by the rms value of an alternating current?

Answer 1

Hint:Alternating current's root mean square, or R.M.S. value, is defined as the value of steady current that would create the same amount of heat in a given resistance in a given time, as A.C. current would when sustained across the same resistance for the same duration.

Complete answer:
The square root of the mean square (RMS) is defined as the root mean square (RMS) in mathematics and its applications (the arithmetic mean of the squares of a set of numbers).The quadratic mean, commonly known as the RMS, is a special instance of the generalised mean with exponent 2.

RMS may alternatively be expressed as an integral of the squares of the instantaneous values throughout a cycle for a continuously changing function. RMS is equivalent to the value of the constant direct current that would cause the same power dissipation in a resistive load for alternating electric current.

Alternating current is described as a current whose magnitude varies over time and periodically reverses direction. The RMS value of alternating current is defined as the amount of heat created by a steady current running through a circuit for the same length of time as an alternating current flowing through the same circuit for the same amount of time.

The Root-Mean-Square of instantaneous current values is known as RMS. Direct current flowing through a resistance provides the RMS value of alternating current. AC has an RMS value that is higher than the norm. The area covered in half-cycles may be used to calculate the RMS value of a sine current wave. This holds true for all waves, including sinusoidal, non-sinusoidal, symmetrical, and asymmetrical waves.It is given as \[{I_{r.m.s}}\; = \;\dfrac{{{I_0}}}{{\surd 2}} = \;0.707\;{I_o}\].

Note:Peak value is defined as the highest value achieved by an alternating quantity in a single cycle. The average Value is calculated by taking the average of all the instantaneous values of an alternating voltage and current during one complete cycle. The rms value is calculated by taking the square root of the means of squares of instantaneous values.