Problem SG 43
Problem SG 43
Consider the two sinusoid voltages below. For what amplitude will wave B have the same power as wave A?
In[]:=
PA=Power[RootMeanSquare[Table[0+1Sin[2Pi(1/2)t],{t,0,2,0.001}(*Table*)](*RMS*)],2(*Power*)]
Out[]=
0.49975
Wave B swings from 0 V to some peak value. Let this peak be 2x V. Therefore the DC offset will be x and the amplitude (which is the swing around the DC offset is also x). Equate the power in wave A to the power in wave B and solve.
In[]:=
Solve[PA==Power[RootMeanSquare[Table[x+xSin[2Pi(1/2)t],{t,0,2,0.001}(*Table*)](*RMS*)],2(*Power*)],x]
Out[]=
{{x-0.577254},{x0.577254}}
The answer we are looking for is,
In[]:=
%[[2]]
Out[]=
{x0.577254}