Calculate RMS Value of Sawtooth Voltage in Figure 33.54

[oooride]

I'm confused on how to approach this question..

Show that the rms value for the sawtooth voltage shown in Figure 33.54 is Delta V_max / sqrt 3.

All Figure 33.54 shows is a graph of Delta V vs time with amplitudes of +Delta V_max and -Delta V_max with the sawtooth wave going between the amplitudes three times, starting at -Delta V_max and ending at -Delta V_max.


How would I go about starting this question? The only thing I can think of using to start is, Delta V_rms = Delta V_max / sqrt 2 = .707 * Delta V_max. I have no idea how or why I should use this though.. I'm completely stuck..

Any help is greatly appreciated.

Thanks in advance.

 

[AKG]

I'm confused on how to approach this question..

Show that the rms value for the sawtooth voltage shown in Figure 33.54 is Delta V_max / sqrt 3.

All Figure 33.54 shows is a graph of Delta V vs time with amplitudes of +Delta V_max and -Delta V_max with the sawtooth wave going between the amplitudes three times, starting at -Delta V_max and ending at -Delta V_max.


How would I go about starting this question? The only thing I can think of using to start is, Delta V_rms = Delta V_max / sqrt 2 = .707 * Delta V_max. I have no idea how or why I should use this though.. I'm completely stuck..

Any help is greatly appreciated.

Thanks in advance.

$$V_{rms} = \sqrt{\frac{1}{T}\int_0^T [V(t)]^2 dt$$

I believe this is the equation to find the rms (root mean squared) of anything, so you can replace V with f, I, or anything to find rms-frequency, -current, etc. If you look at the equation, it should be clear why it's called root mean squared. T is the period, V(t) is the voltage at t. A sawtooth voltage will just increase linearly over one period, something like V(t) = mt + b (your basic linear relationship). You can easily square this [ V(t) = (mt + b)^2 = (m^2)t^2 + (2mb)t + b^2 ], and integrate from 0 to T, and then divide by T, then take the root. That should be your rms Voltage. I'm pretty sure, at least...

 

[turin]

$$V_{rms} = \sqrt{\frac{1}{T}\int_0^T [V(t)]^2 dt$$

I believe this is the equation to find the rms (root mean squared) of anything, ...

This is indeed correct, with one generalization that is probably not important here since there should be a clearly recognizable period, T.

 

[Gza]

Oh man, I remember having to find that rms value in my lab class a few weeks ago. Not fun.