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1. Why does the rms of alternating current equal the value of dc in a dc circuit for the same power?
2. (Original post by Paranoid_Glitch)
Why does the rms of alternating current equal the value of dc in a dc circuit for the same power?
A good question. This first post on here explains it well talking about RMS voltage (which is equally applicable to current).

https://www.quora.com/Is-DC-voltage-...f-yes-then-how

If you're unsure with what he says, ask me and I'll try to clarify it
3. (Original post by Paranoid_Glitch)
Why does the rms of alternating current equal the value of dc in a dc circuit for the same power?
The r.m.s. value is quoted as a d.c. equivalent of the averaged a.c. signal.

In other words, the r.m.s. value of a time varying non-uniform amplitude/frequency a.c. signal is such that an equivalent d.c. value would produce the same power dissipation in a given load.

It's a bit like saying the power output of a horse ploughing various fields in different weather conditions averaged over a time period is the equivalent of a 750W d.c. motor operating continuously with a constant load.

The former is hard to define without quoting complex measurement conditions, the latter is almost trivial and simplifies analysis and computations.

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