I was trying to choose a resistor value for a pull-up resistor I will use in my project. The project will have I2C communication and SMBus communication. When I was searching on the internet, I have seen some sentence that says using low resistor value for a pull-up resistor causes higher energy consumption. Is it the only disadvantage? If the only advantage of using a pull-up resistor is to reduce energy consumption, would the SMBus or I2C communication work without any pull up resistor? And how much energy does it save if I use 2 k pull up resistor, would it reduce consumption drastically? Thanks beforehand.
You do need a pull-up. And 2k is a low value so it will consume more power than 10k would. You need to select your pull-up to have the rise time small enough to be within specifications that depend on the clock speed, bus capacitance, current driving ability of the chips and their voltage levels to determine bus being high or low.