# How do I calculate the root mean square voltage of a square wave (with drawing)?

I need to find the root mean square voltage based on this drawing, knowing that the period (T) is equal to 6 seconds, and the voltage (V) is equal to 14 Volt. I know that the rms can be calculated using this formula. How do I apply this into my exercise?  knowing that T = 6s, V = 14V find rms voltage.

• @muyustan try to stay away from "google that comments" meta.stackexchange.com/questions/15650/… – Voltage Spike Jun 23 '20 at 22:58
• If this is homework, please provide a solution to the problem as required by site guidelines – Voltage Spike Jun 23 '20 at 22:59
• @VoltageSpike don't agree, but rules are rules, noted. Your comment in which you tagged med did not bring a notification to me by the way. – muyustan Jun 24 '20 at 7:36

## 2 Answers

You have the formula right there, integration is indeed the area under the curve. Over one period, you just have to calculate the area under the voltage waveform/curve squared. It is pretty clear that the time duration between T/4 and T will be 0 even when squared. And you have,

$$V^2 * T/4$$ of area remaining. Inserting V=14 and T=6, $$14*14*6/4 = 294$$ now multiply it with 1/T. $$294*1/6 = 49$$ It is now only a matter of solving the following equation, which I'll leave as an exercise.

$$V_{rms} = \sqrt{49}$$

• Volts not amps unless you meant (A)mplitude. – Andy aka Jun 24 '20 at 8:29
• @Andyaka Yes I also wanted to write $$V_{rms}$$ but the formula in the question had $$A$$ in left hand side. But you are right that $$A_{rms}$$ does sound like rms current magnitude. It is best to convert A to V. – muyustan Jun 24 '20 at 9:08
• oh god, how can I write inline mathjax – muyustan Jun 24 '20 at 9:09
• @muyustan use \$instead of $$– JRE Jun 24 '20 at 9:22 • @Andyaka oh my english, could not understand your "tone" exactly, but, I am taking that as a real question, I did not force a linebreak, assumingly, $$lorem ipsum$\$ is get printed in a new line automatically. – muyustan Jun 24 '20 at 10:50 I hope that you can read my terrible hand writing.