All the resistors available come with a finite amount tolerance. This is undesirable particularly in highly sensitive systems. While we can use resistors with the least tolerance available, I want to know if there are any methods (something like designing a special setup to bring down the tolerance) using which we can manually reduce the tolerance value to the minimum that we may require?
Answer
Tolerance is a statistical abstraction which tells us how much variation to expect from a sample of resistors of a given type. A single resistor doesn't have tolerance: it has a value, which deviates to some extent from the stated value (and of course varies with temperature). We cannot change (manually or otherwise) a property that a part doesn't have.
If part of a circuit requires a very accurately set resistance (which perhaps has to compensate for variations in other parts, and so cannot be a fixed value, no matter how precise), we can use a potentiometer. A potentiometer or rheostat is a resistor whose value you can manually change.
A useful trick is to use a fixed resistor for most of the resistance, and a smaller-valued potentiometer just for the adjustment. For instance, if we wanted to adjust 100K within a +/- 5% range, we could get a 95.3K resistor (E48 series number), and a 10K potentiometer wired as a rheostat in series with that resistor.
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