Hi,
Measurements of rectifier circuits is a little tricky because the diodes only conduct for part of the time, and that could be a very small part of the time. This means a measurement of the voltage alone is not enough.
The exact way is to multiply each voltage point in time with each current point in time, sum the results over one cycle, then divide by the time of one cycle. This can be done using a scope or using an ADC that is fast enough to sample both current and voltage. Because most power supplies operate at 50Hz or 60Hz the ADC really doesnt need to be super fast. 100 points would only require about 6000 samples per second. That's cake in the ADC world.
Alternately you could estimate the current waveshape as a pulse (as viewed on a scope) and go from there.
These kinds of problems are often not very intuitive, in that they are not as simple as they look sometimes. A test tells us for sure if we can use the Vrms*Irms approximation. This test is simply a test to see if the square of the integral of v*i is equal to the product of the integral of v squared times the integral of i squared.
If the following equality is satisfied, then we can use the Vrms*Irms method (Tp is total period):
integrate(i(t)*v(t),t,0,Tp)^2=integrate(i(t)^2,t,0,Tp)*integrate(v(t)^2,t,0,Tp)
If that is not satisfied, then the accuracy will depend on how far off the right hand side is from the left hand side, so if we introduce a factor A^2:
A^2*integrate(i(t)*v(t),t,0,Tp)^2=integrate(i(t)^2,t,0,Tp)*integrate(v(t)^2,t,0,Tp)
If A is between (0.99) and (1.01) for example, then the accuracy is within 1 percent. If A is between (0.98) and (1.02) then the accuracy is within 2 percent, and note we look at A not A^2 which is actually in the formula. You see how this works
In reality though we often deal with waveforms that are only non zero for part of the total time period Tp, so we really have:
A^2*integrate(i(t)*v(t),t,0,Tp)^2=integrate(i(t)^2,t,0,T1)*integrate(v(t)^2,t,0,T2)
where the limits of integration have been changed to show the real limits, and that is assuming the waves both start at t=0 (to make it different than that would require a more complicated expression which would only make it harder to comprehend what the difference is).
Some expressions work out very well because the waveshape is compatible with the Vrms*Irms approach. This includes complete sine waves. For two sine waves in the first equality above the two sides always equal each other exactly so that always works for sine waves as long as they are not interrupted. In the second expression T1=Tp and T2=Tp, and so A=1 which means perfect equality.
Pulse or nearly pulsed waveforms are tricky so it helps to have a test to make sure the Vrms*Irms approach is applicable.