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## Homework Statement

The mill (single phased) is now affected by a load from a resistor. We assume that the turbine can deliver an infinitely large current without affecting the frequency.

figure 1 illustrates the load:

http://puu.sh/19GGR [Broken]

The voltage over the capacitor can can be expressed as

V

_{0}(t) = Re(v

_{p}* e

^{i*ω*t})

where ω is the angular frequency, i is the complex number, and v

_{p}is a complex number (also called a phasor) and can be expressed as

v

_{p}= k * [itex]\frac{1}{1+iω*R*C}[/itex]

The values R and C

_{k}er unknown, but can be assumed to be constant and real.

**Make an expression for V**

_{0}(t) where only the real part is described.**Rewrite the expression for V**

_{0}(t) to the form V_{0}(t) = A * cos(ω_{ω}*t + θ_{ω})Where A is the amplitude

## The Attempt at a Solution

As for the first part, my idea was to rewrite the exponential part e

^{i*ω*t}to cos(t*ω)+i*sin(t*ω) and then multiply it with v

_{p}as you would with two complex numbers, and then simply discard the imaginary part..

which gives me [itex]\frac{k*cos(t*w)}{1+w*R*C}[/itex]

But im pretty sure im way off.. and I could use some help!

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