# Output Voltage, AC Source

## Homework Statement

The rms output voltage of an AC source is 180 V, and the operating frequency is 90 Hz. Write the equation giving the output voltage as a function of time t. (Use t as necessary.)

## Homework Equations

$$(\Delta v) = (\Delta V_{max})sin\omega t$$
$$\Delta V_{max}= \sqrt{2}V_{max}$$
$$\omega = 2\pi f$$

## The Attempt at a Solution

I thought it was a simple solve for the values of omega, Vmax, and plug those into the first equation, but I am apparently wrong according to the website. I don't think I have messed up. The only other thing I can think of is that they want it in cosine instead of sine. I got the following answer:

Voutput = 255sin(566t)

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Bump.

LowlyPion
Homework Helper
Vrms = Vp/√2

Vt = Vp*sin(ωt) = √2*Vrms*sin(2*π*f*t) = 254.55*sin(565.48*t)

That's the way I figure it.

It's difficult to imagine that they would be picky about that small a rounding error.

I meant that with my one equation...I meant that Vmax = sqrt(2)Vrms. And...I know it must be right, they are just being picky about how it's typed in, yet, I get the same answer you get. It shouldn't be cosine (thought it could be, but would require a phase angle). It also shouldn't be negative as far as I can tell. And, as my answer is within 1% of your answer, it shouldn't be picky about that either. I will just try one other thing and then email my teacher about it.