[sdiy] Power Supply Questions

[Oscar Salas]

Other question regarding power supplies is about the RMS current depending of the ripple after capacitors...

Depending of the ripple, there will be more or less charging time for each cycle (10ms Europe).
And for example for a 1A output, a big ripple that has, say 1/5 of the cycle time for charge the capacitors, current will enter in pulses of 5A, but also for a 1A output, a little ripple that has, say 1/20 of the cycle time for charge the capacitors ,current will enter in pulses of 20A.
But we are interested in RMS current.
I understand that in both cases RMS current is the same =1A... it is not logical?
But the "Student Manual for the Art of Electronics" by Hayes and Horowitz in page 73, says that moderate ripple results in lower RMS current.
There is a formula following my previous examples, 
For 1/5 cycle time charging capacitors: Irms=(1/5[5A]^2)^1/2=√5A=2.2A
For 1/20 cycle time charging capacitors:Irms=(1/20[20A]^2)^1/2=√20A=4.4A
Could someone explain this equation or explain why this happens?