Electricity supply in homes is AC but what about rms value that has only one direction? In our homes, electricity supply is AC.but we have rms value in our homes...How do they relate? Is rms value generated in transformer or what??
 A: The rms value of an alternating voltage is a particular type of average. It is equivalent to sampling the the voltage at many equally spaced times throughout a cycle (getting $V_1$, $V_2$, $V_3$ ... $V_n$), squaring these values (getting $V_1^2$, $V_2^2$, $V_3^2$ ... $V_n^2$), finding the ordinary mean of these values:
$$\text{mean square voltage} =\frac{V_1^2+V_2^2+ V_3^2 ... +V_n^2}{n}$$
The rms (root mean square) voltage is the square root of this mean square voltage, so
$$\text{rms voltage} =\sqrt{\frac{V_1^2+V_2^2+ V_3^2 ... +V_n^2}{n}}$$
The squaring of the voltages means that any negative voltages generate positive numbers, and that is the reason why the rms value is positive.
A: RMS stats for Root-Mean-Square. You have a varying quantity, you then CALCULATE the Root-Mean-Square value of this varying quantity.
The importance of rms value of AC is that, physically the RMS value of AC circuit is equivalent to a DC circuit that has voltage and current same as the rms values.
A: The rms voltage is a measure of the average voltage of an AC supply - it is not a different type of current supply. The rms or “root mean square” voltage is usually the value that is used to specify the voltage of an AC supply because:

*

*The actual voltage varies over time, at a rate determined by the frequency of the supply.

*The average or mean voltage is zero, because the voltage alternates between positive and negative values.

*The rms voltage is more useful than the peak-to-peak voltage (difference between maximum and minimum voltages) because it has a simple relationship with the average power delivered by the supply - the average power delivered for a load of $R$ ohms is

$$\displaystyle P_{avg} = \frac {V_{rms}^2}{R}$$
