i have learned what is rms value just before . its has been stated like"power dissipated with rms voltage is same power dissipated by equivalent dc voltage".i understand this point. Later question arose to me why we need rms value of signal and i accommodate myself that is to make analyses simple. But i want strong answer why we are interested in Rms value.?
Because we are often interested in the power associated with a signal and rms is directly related to the power associated with a signal.
yes i agree we always interested in power and doesn't energy provide any usefull information? i cant imagine clearly how its could you say how its related briefly?
I assume you know how voltage, current, and power are related for a DC circuit. For an AC circuit, with a resistive load, they are related in exactly the same way, if and only if, you use RMS voltage and RMS current. Any other choices of values for voltage and current give results that are inconsistent with reality. The way we can be certain of this is by having a resistive heater warm up a quantity of water. A given DC voltage and DC current give a rise of say 10°C. The numerically identical RMS voltage and RMS current give the very same temperature rise as the DC example. Two things which produce the same result must be equivalent.
It is related by definition. The effective voltage (or current) of a waveform is that value that, if delivered by a constant voltage (or current) source would deliver the same average power to a purely resistive load. If you use that definition, you then find that the effective voltage (or current) is equal to the square root of the mean of the voltage (or current) squared, hence the name RMS.
Use it to find rms current in the circuit at that point. Use it to find the reactive power associated with the capacitance. Use it to find the rms voltages at other points in the circuit. And on and on.