Solution SG 41

Two resistors carry the currents shown below. Which is warmer?
To answer this problem we need to calculate the heat (power) dissipated in the resistors. Since the resistors are identical we can assume unit resistance. Power = Irms^2*1.
In[]:=
P1=Power[RootMeanSquare[Table[0.5Sin[2Pit],{t,0,1,0.001}](*RootMeanSquare*)],2(*Power*)]
Out[]=
0.124875
In[]:=
P2=Power[RootMeanSquare[Table[0.5+0.5Sin[2Pit],{t,0,1,0.001}](*RootMeanSquare*)],2(*Power*)]
Out[]=
0.374875
So the circuit on the right hand side is warmer because it dissipates more power.