# RMS Current

1. Apr 25, 2007

### chaoseverlasting

1. The problem statement, all variables and given/known data

If the instantaneous current is given by I(t)=3+4sinwt, what is the value of rms current?

3. The attempt at a solution

I thought rms value was max val/1.414. The answer I got was $$\frac{7}{\sqrt{2}}$$. The answer given is $$\sqrt{17}$$. Why?

2. Apr 25, 2007

### Curious3141

Actually, the first principles definition of RMS value of a current I(t) with periodicity T is

$$I_{rms} = \sqrt{(\frac{1}{T})\int_0^T{{I(t)}^2}dt}$$

RMS is Root-Mean-Square. That's exactly what that expression represents, written from left to right. When you evaluate it, you work from inside outward, i.e. square the current, take the mean, then take the root.

Review the derivation of the expression for the RMS of a simple sinusoidal waveform e.g. $$I(t) = I_0\sin{(\omega t)}$$ and use that method to work out the RMS here. You will need trig identities to simplify then integrate (everything becomes simple at the end because of the bounds of integration).

3. Apr 25, 2007

### chaoseverlasting

Thank you. I knew I was being pigheaded here. I got it now.