In Alternating Current (AC) system magnitude of electrical quantities are expressed in root mean square (rms) values.
In Direct Current (DC) system, magnitude of current or voltage is constant over the period of time. We can specify that 5A current is flowing or 12V potential difference is existing between two points. For example, DC 5A is shown below, Red being positive and black being negative. In this image, one AC signal is also shown in Blue colour.
The question is: at which point we should specify the current as it is continuously varying and changing its sign from +ve to -ve and -ve to +ve in each cycle. One of the approach may be specifying peak value:
The problem with peak value is that, in actual, it appears for a fraction of time in a cycle (two time in a cycle, one in +ve and another in -ve). for rest of the cycle, magnitude is less than peak value. If we compoare 5A DC and 5A AC (peak value), DC current will have more power over a period of time. That is how concept of RMS value came. It is value of AC signal, for which same value DC signal dissipates the same power in a resistor.
For understanding rms value,
let us calculate actual energy dissipated in heat for one cycle of AC. First divide
AC cycle in "n" parts on time scale. Calculate energy of each part by
formula I2Rt and add them up over the period of one cycle.
In above image energy for one cycle will be I12Rt1 + I22Rt2 + I32Rt3 +…e In2Rtn
Energy (over one cycle) E = (I12Rt1 + I22Rt2 + I32Rt3 +…. In2Rtn)
In the above equation t1
=t2 =t3 …=tn =t
Energy (over one cycle) = (I12
+ I22 + I32 +….
In2) Rt
Average energy for nth part
Energy (for nth part) = (I12 + I22 + I32 +…. In2) Rt /n
Power (for nth part) = E/t = (I12 + I22 + I32 +…. In2) R /n …EQ1
As we know Power P = I2R …EQ2
From EQ1 and EQ2:
I2R = (I12
+ I22 + I32 +….
In2) R /n
I2 = (I12
+ I22 + I32 +….
In2)/n
I = √ {(I12 + I22
+ I32 +…. In2)/n}
- 200V means 200V RMS value
- 10A means 10A RMS value
- 200Vpeak means 200V peak value
- 10Apeak means 10A peak value
- Sine wave: RMS value = Peak value / √2
- Square wave: RMS value = Peak value
- Saw tooth wave / triangle wave: RMS value = Peak value / √3
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