Final answer:
To determine the value of a resistor that has overheated and turned black, use a multimeter once the resistor has cooled and is safe to handle. If the color bands are unreadable due to damage, circuit documentation or replacement with a known specification is required. This overheating suggests circuit issues that must be addressed.
Step-by-step explanation:
To determine the value of a resistor that has turned black due to excessive heat, you should first ensure the resistor is disconnected from any power source and has cooled down to avoid injury. The most accurate method to find the resistor's value is by measuring it with a multimeter, which is a tool that can measure electrical properties including resistance.
If the resistor is too damaged for a multimeter reading and the color bands are still visible, you could use those color bands to determine resistance. However, if the color bands on the resistor are not visible due to the damage, and assuming you cannot get an accurate reading with a multimeter, you might have to refer to the circuit's documentation or replace the resistor with one of a known similar specification, presuming the reason for the burnout has been addressed.
It's important to note that excessive current can cause a resistor to overheat, potentially leading to a change in its physical state, which may include blackening or even destruction of the resistor. Such conditions indicate that there are issues with the circuit that need to be resolved to prevent future damage.