# Root mean square current

1. Sep 1, 2007

### Vaman Hegde

Am sorry, if this topic does not belong to this section, as i am new, kindly oblige
Can root RMS value of current (what we study in Alternating currents) be negative?
i feel that it can surely be negative as it is a root, but my teacher told that it can't be negative and showed just one line above x axis. When asked he told me that it's a root of mean of square, hence can't be negative. i did not understand, kindly help......

2. Sep 1, 2007

### Archduke

The rms is the average of the squares, square rooted. Or, Mathematically:

$$x_{\mathrm{rms}} = \sqrt {\frac{x_1^2 + x_2^2 + \cdots + x_n^2}{n}} =\sqrt {\frac{1}{n} \sum_{i=1}^{n} x_i^2}$$

So, as you can see from the formula, the squaring of the $$x_i$$ means any information about the sign of the number is lost. Basically, the root mean square is a measure of the magnitude of a set of numbers.

3. Sep 1, 2007

### leright

Well, when you square a sinusoidal current with zero dc offset you get a waveform that is always positive. Therefore, the average of this always positive waveform is also positive. Technically, the square root of a positive number can be both positive and negative, of course, but the root operation in the RMS calculation is the PRINCIPAL square root, which is the POSITIVE root. So, your teacher is right, the RMS current is a positive value.

4. Sep 1, 2007

### rootX

it's my name.