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# An ac voltage is given by e=3+4sin(wt+π/3). Calculate the rms value of voltage

2 years ago

The effective value is the RMS value. Let’s work this out for any combination of DC plus AC, ie: for  a+bsin⁡(ωt).

The square of this is:

a2 + 2 a b sin ⁡ ( ω t ) + b2 sin2 ( ω t )

Using the trig identity  sin2 ( x ) =( 1/ 2) ( 1 − cos ⁡ ( 2 x ) )

this becomes:  a2 + 2 a b sin ⁡ ( ω t ) + b2/ 2 ( 1 − cos ⁡ ( 2 ω t ) )

Next we need to take the mean. However both sine and cosine have a mean of zero and so we can ignore these terms, leaving us with a mean of simply:  a2 + b2 / 2  As this is constant then the mean has the same value. Finally we take the root, giving the RMS value: