#sinusoids

[grrl-beetle]

sinusoids v1.7.5 by Adrian Freed

[cellimagelibrary]

Hold the Onions! Image of the Week - July 10, 2017

CIL:39088 - http://www.cellimagelibrary.org/images/39088

Description: This scanning electron micrograph shows the internal structure of liver tissue from an adult mouse. The sinusoids (vascular channels lined with endothelial cells) can be seen as pink structures running through the tissue. These contain red blood cells and Kupffer cells (specialized macrophages of the liver). Hepatocytes, shown in brown, are arranged in plates surrounding the sinusoids. Bile is secreted into the canaliculi, shown as green channels. These are dilated intercellular spaces between adjacent hepatocytes and bile flows through them en route to the small intestine.

Author: EM Unit, UCL Medical School, Royal Free Campus and Wellcome Images

Licensing: Attribution-NonCommercial-NoDerivs 2.0 UK: England & Wales (CC BY-NC-ND 2.0 UK)

[nevermorethis]

it's been a part of me since i can remember

and i'm so tired of it

all i wish for

is to be common and simple

as others are

but i'm afraid that the only way to do it

is to never feel again

your skin

my bed

your touch

my warmth

your heartbeat

my heartbeat

[noahsarc2-blog]

Our math teacher almost exclusively writes in this green marker.

Green is the opposite (complimentary color) of red.

She draws sinusoid graphs with them.

Sinusoid graphs look like water/waves.

Red or green water.

Recap: The following are important

Red

Green

Water (as we already knew from the arcs and Too Close for Comfort, etc.)

Our math teacher may be involved

[el3ctron]

Triple interpretación del renderizado atómico en nuestro superservidor de simulación.

[thewvnderer]

(via https://www.youtube.com/watch?v=ZjMR8KU6YEc)

[engineeringtldr]

So let’s start putting all this stuff together. We’re given the circuit above and told that the frequency is 50 Hz. We’re then asked to find the current.

First, let’s get the voltage source into a format more useful to us. We’ll convert it to polar form, and while we’re at it, we’ll get the angular frequency, ω.

Next, we need to figure out the circuit’s impedance. We’ll need ω to do this.

We’ll convert this to polar form too.

Finally, we can apply Ohm’s Law the same way we did with resistive circuits, using impedance in place of resistance. Having both the voltage source and the impedance in polar form allows us to divide them easily and gets us a current in polar form.

This is pretty straightforward. Let’s take a look at what happens if you raise the frequency. Let’s say the frequency is 500 Hz. It won’t change the magnitude and phase of the voltage source, but it will change the circuit’s impedance.

The impedance we got before at 50 Hz was mostly capacitative - the j term was negative. At a higher frequency, though, it behaves more like an inductor as the j term goes positive. Individually, the capacitor’s impedance drastically decreased with higher frequency, and the inductor’s impedance drastically increased. This will result in a much different current at this higher frequency.

[engineeringtldr]

More Than You Ever Wanted to Know About Electrical Engineering, Part 23: Working With Impedances

If you’re dealing with a complex network, you can combine impedances in series and parallel just as you can with resistance, capacitance and inductance. Impedances combine like resistances: for series combinations, they add, and for parallel combinations, the inverse of the total impedance is the sum of the inverses of the component impedances.

You can also use a more general version of Ohm’s Law to deal with impedances. Instead of just resistance, we can now relate voltage, current, and impedance.

If Ohm’s Law holds true, that means that KVL and KCL also hold true. With an understanding of impedance, we can essentially treat complex circuits involving capacitance, inductance, and time-varying sources as if they were simple DC circuits containing only resistances. This will make our lives a thousand times easier. The only tricky part is translating the voltage, current, and impedances you’re given into a form that will let you manipulate them easily.