Half wave rectifier

  • Thread starter kimmy510
  • Start date
8
0
while finding Vrms or Vavg we use integration and we use d(wt) and integrate between the limits 0 to 2pie. When 'w' is a constant how can we take it as d(wt).and if we take as d(wt) only then why are the limits not changed to 0 to 2(w)(pie)?
 

uart

Science Advisor
2,776
9
Yes you're kind of right. You would change the limits of integration as appropriate. But remember that the original limits of integration would normally be t=0 to t=T (the period). But T = 2 Pi / w therefore wT = 2Pi is new limit after the change of variable.

Mathematically when we make the substitution [itex]\theta = \omega t[/itex] we get:

[tex]\int_{t=0}^T f(\omega t) \, dt = \int_{\theta=0}^{\omega T} f(\theta)\, d\left(\frac{\theta}{\omega}\right) = \frac{1}{\omega} \int_0^{2 \pi} f(\theta) \, d\theta [/tex]
 
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