The datasheet of the 24LC256 EEPROM states that:


  The SDA bus requires a pull-up resistor to VCC (typical 10 kΩ for 100 kHz, 2 kΩ for 400 kHz and 1 MHz).


I thought that any resistor with a kΩ value would do the job (and it seems that my EEPROM works fine at different frequencies with a 10 kΩ resistor).

My questions are:


is there a correct value for pull-up resistors ?
is there a law/rule to determine this value ?
how do different resistance values affect the I²C data bus ?


The correct pullup resistance for the I2C bus depends on the total capacitance on the bus
and the frequency you want to operate the bus at. 

The formula from the ATmega168 datasheet (which I believe comes from the official I2C spec) is -- 

$$\text{Freq}<100\text{kHz} \implies R_{\text{min}}=\frac{V_{cc}-0.4\text{V}}{3\text{mA}}, R_{\text{max}}=\frac{1000\text{ns}}{C_{\text{bus}}}$$

$$\text{Freq}>100\text{kHz} \implies R_{\text{min}}=\frac{V_{cc}-0.4\text{V}}{3\text{mA}}, R_{\text{max}}=\frac{300\text{ns}}{C_{\text{bus}}}$$

The Microchip 24LC256 specifies a maximum pin capacitance of 10pF (which is fairly
typical). Count up the number of devices you have in parallel on the bus and
use the formula above to calculate a range of values that will work. 

If you are powering off of batteries I would use values that are at the high
end of the range. If there are no power limits on the power source or
power dissipation issues in the ICs I would use values on the lower end
of the range. 

I sell some kits with an I2C RTC (DS1337). I include 4K7 resistors in the kit which 
seems like a reasonable compromise for most users.
