So I'm pretty new to electronics and just started playing around with the Arduino to learn the basics. In one of the projects there was just a simple button and 3 LEDs that are controlled by the Arduino. Following is the schematic:
As there is no explanation in the book as to why there's a 10KΩ resistor, I did some Googling as to why it's there. I found out it's a voltage divider and keeps a 5V \$V_{out}\$ into the Arduino 2 pin.
My question is, is this resistor necessary? I know it follows the following equation:
$$ V_{out} = V_{in} \times \dfrac{R_2}{R_1 + R_2} $$
So if there's no \$R_2\$, I'd be dividing 0 by 0. In which I'm guessing it's a short circuit? But any resistor of like 1Ω would still allow the 5V \$V_{out}\$. Which would mean that any resistor avoids short circuits? What if I don't connect it to ground at all? Can't it flow just directly from 5V to pin 2 through some internal ground?
I'm kind of reluctant to just try it out myself and see what happens out of fear I'm going to fry some components.