Topics for an explaining a concept essay

Square root ~ 7 
 
With more intervals the rms average turns out to be ( peak value ) / √2 =  peak value / = peak value  
 
2  For those who are familiar with the graphs of sine and cosine functions, then the following algebraic method can be attempted. 
 
I  =  I o sin  ωt and  I 2  =  I o 2  sin 2 ωt  
 
The heating effect depends on  I 2 R , and so an average of  I 2  is needed and not an average of  I
 
To find the rms value, you need the average value of sin 2  as time runs on and on. 
 
The graph of sin ωt  and the graph of cos ωt  look the same, except for a shift of origin. Because they are the same pattern, sin 2 ωt  and cos 2 ωt  have the same average as time goes on. 
 
But sin 2 ωt  + cos 2 ωt  = 1. Therefore the average values of either of them must be 1/2. 
 
Therefore the rms value of  I o sinω t  must be  I o  / √2  
 
The rms value is times the peak value, and the peak value is times the value the voltmeter shows. The peak value for 230 V mains is 325 V. 
 
3  Alternatively: Plot a graph of sin 2 θ . Cut the graph in half and turn one half upside down, or copy onto a transparency and fit together. The two halves fit together exactly, showing that the mean value is 1/2.

Topics for an explaining a concept essay

topics for an explaining a concept essay

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