why did we use the rms value ? because he didn\'t ask for rms. Determining Avera

Question

why did we use the rms value ? because he didn't ask for rms.

Determining Average Power Delivered to a Resistor by Sinusoidal Voltage Example 10.3 nusoidal voltage having a maximum ampli- ide of 625 V is applied to the terminals of a a) A sinusoidal tude of 625 50 resistor. Find the average power delivered to the resistor. Eq. 10.19, the average power delivered to the 50 resistor is (441.94) (44194)2 = 3906.25% P = =3905.25 W. 50 Repeat (a) by first finding the current in the b) The maximum amplitude of the current in the resistor. resistor is 625/50, or 12.5 A. The rms value of the current is 12.5/V2, or approximately 8.84 A. Hence the average power delivered to Solution the resistor is ) The rms value of the sinusoidal voltage is P = (8.84)250-390625 W. 625/ V2, or approximately 441.94 V. From

Explanation / Answer

GIVEN VOLTAGE SOURCE IS A SINUSOIDAL WAVEFORM (I.E AC SOURCE )

If we made an attempts to find an average value of AC ,we would directly get the the answer zero over a period of time

AVERAGE VALUE

Average value is nothing but the area of the waveform over a period

For a periodic waveform, the area above the horizontal axis is positive while the area below the horizontal axis is negative. The result is that the average or mean value of a symmetrical alternating quantity is zero because the area above the horizontal axis (the positive half cycle) is the same as the area below the axis (the negative half cycle) and cancel each other out in the sum of the two areas as a negative cancels a positive producing zero average voltage.

Then the average or mean value of a symmetrical alternating quantity, such as a sine wave, is the average value measured over only half a cycle since over a complete cycle the average value is zero regardless of the peak amplitude.

SO avearge value is not used in power calculations,to overcome this we are using a mathematical concept RMS value

RMS VALUE

This RMS is a mathematical quantity (used in many math fields) used to compare both alternating and direct currents (or voltage) and it is the average of all the instantaneous areas taken under the curve over a given period of the waveform

The RMS value of AC (current) is the direct current which when passed through a resistor for a given period of time would produce the same heat as that produced by alternating current when passed through the same resistor for the same time.

The same thing is applicable to voltage also

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