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## Homework Statement

Hello,

I was wondering if anyone could confirm my work for the following graph:

I'm supposed to find the rms for 1 complete cycle (0, 10ms)

The time constant is 1ms.

Charging phase, v=1-e^(-t/1ms)=1-e^(-1000t)

discharging phase, v=e^(-1000t)

## The Attempt at a Solution

First, I find the rms contribution for the charging stage.

[tex]\sqrt{\frac{1}{10^{-3}}\int ^{5(10)^{-3}}_{0}{(1-e^{-1000t})^2dt}}=\sqrt{\frac{1}{10^{-3}}(t-\frac{e^{-2000t}}{2000}+\frac{e^{-1000t}}{500}|^{5(10)^{-3}}_{0})}=0.59274 V[/tex]

Next, I found the contribution of the discharge phase:

[tex]\sqrt{\frac{1}{10^{-3}}\int ^{5(10)^{-3}}_{0}{(e^{-1000t})^2dt}}=\sqrt{\frac{1}{10^{-3}}(-\frac{e^{-2000t}}{2000}|^{5(10)^{-3}}_{0})}=0.707091 V[/tex]

and the effective rms for the entire cycle is

[tex]v_{rms}=\sqrt{(0.59274 V)^2+(0.707091 V)^2}=0.923 V[/tex]

Or do I have to multiply each of the functions underneatht he the sqrt by a factor of 5(10)^-3 ?

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