I was studying about alternating current, and I stumbled upon RMS. I clearly cannot understand what it means, the only thing my textbook says is: RMS current $I$ is related to the peak current $i_m$ by $ I=0.707 i_m$
Why are we multiplying AC current by $0.707$?
Are there any sort of things I've missed learning?
"RMS" refers to "root-mean-square." It's one particular way of taking an average magnitude of something. In particular, the RMS of x is given by:
$$ x_{rms}=\sqrt{\langle x^2\rangle}$$
Where $\langle a\rangle$ denotes the average of $a$. Or, to put that in words, it's the square root of the average of $x$ squared.
For a sinusoidal wave with current $I=i_m\sin\omega t$, the RMS current is given by:
$$I_{rms}=\sqrt{\langle i_m^2\sin^2\omega t\rangle}$$
which simplifies to:
$$ I_{rms}=i_m\sqrt{\langle\sin^2\omega t\rangle}$$
$\langle\sin^2\omega t\rangle={1\over2}$. You can see this in a number of ways, for instance by considering $\sin^2\omega t+\cos^2\omega t=1$ and that $\sin$ and $\cos$ are just shifted versions of one another, so they have the same average, or just brute force the math. Putting this together, you get:
$$I_{rms}={i_m\over\sqrt2}\approx.707i_m$$
Note that this means the expression given in your book is only correct for a sinusoidal current.
