# How does wiring resistors in series and parallel affect their errors?

In an experiment I am conducting, I am trying to measure low currents by wiring a radio device in series with a small-resistance resistor setup, composed of 9 of 1 ohm +/- 5% resistors in series and parallel as shown below, resulting in a total of 1 ohm.

By my understanding, resistors are manufactured such that there is a distribution of values centered by the marked value with most of them lying in the +/- 5% range, but in theory, there will always be resistors outside such range.

While in theory (by error analysis formulas) my series-parallel setup would have the same error as each one of the resistors, intuitively, doing so is in essence taking the average of the 9 resistors and thus tightening up that distribution curve, such that the error %age is lowered. This was my intent in doing those 9 resistors as opposed to only 1 resistor.

So my question is: What is the error of the 9 resistor setup? Theoretically, I calculate 5% but by intuition, it is less. If it's the former, I would like to know why, and if it's the latter, I would like to know how to find the final percentage error in this situation. I hope it is the latter so that I can qualify my experimental technique (oh and speaking of which, please assume that the voltage drop of the resistor setup does not drop the current through the circuit).

• dangerousprototypes.com/2010/07/01/… – user3109679 Feb 9 '15 at 0:50
• In my experience, modern carbon- or metal-film resistors will be very close to their marked values. I once measured 50 10K 5% resistors of both metal and carbon film, and probably of different production batches, and the total spread of values was about 1% (spread, low to high, not +/- 1%). The average was just under 10 K, so I concluded my meter read slightly low. It is likely that the older carbon composition resistors had a wider spread, but I don't know if the distribution implied in the dangerousprototypes link was common. – Peter Bennett Feb 9 '15 at 1:22
• For a randomly distributed error, the error goes to zero for series and parallel as the number of resistors increases. For a biased deviation from the expected value, it converges to a constant. physics.stackexchange.com/questions/160764/… – C. Towne Springer Feb 9 '15 at 6:31
• For many enough series resistors, the residual distribution will approach the normal distribution, thus the tolerance standard deviation will decrease by a factor $1/\sqrt{N}$. Although the absolute tolerance stays at the initial value, the probability of coming close to that value (for many enough resistors) eventually becomes so low that it won't happen any time, anywhere in the universe. – HKOB Feb 9 '15 at 12:22