Why doesn't the RMS current and voltage give me average power?

Question

Apologies for the multiple bridge rectifier questions.

I have a 230V/9V 10VA transformer, and I want to know how much DC current I can draw from this circuit. From this I assume that the \$I_{rms\_max} = 1.1A \$.

I ran the simulation for various values of C1 and R1, and this seems to give the greatest possible DC current (I think).

Because this was going to be fed to a boost converter, I allowed 2V ripple.

The following values were obtained from LTspice:

• \$V1_{rms} = 9V\$
• \$I_{V1(rms)} = 0.96A\$ <- Less than 1.1A
• \$V_{out(rms)} = 10.15V\$
• \$I_{R1(rms)} = 0.40A\$

This gives me:

$$ \eta = \frac{P_{out}}{P_{in}} = \frac{10.15*0.4}{9*0.96} = 47\% $$

However, this is the power graph:

The average values of the graphs give me 4.9W and 4.13W, which gives me an efficiency of 84%.

Which value is correct?

Answer 1

Averaging the instantaneous power is the correct approach here.

The product of the rms voltage and current gives the apparent power. The average power is, in general, less than the apparent power due to a less than unity power factor.

See this related question for a detailed answer on the power factor calculation.