Four identical resistors, each of resistance R, are available. A student claims that by arranging the four resistors in some combination of series and parallel connections it is possible to obtain an equivalent resistance equal to 2R. You will evaluate this claim without constructing an explicit circuit.
(a) For two identical resistors of resistance R, identify the arrangement that produces (i) the maximum possible equivalent resistance and (ii) the minimum possible equivalent resistance. For each arrangement, state the value of the equivalent resistance in terms of R.
(b) Explain qualitatively why adding more resistors in series always increases, and adding more resistors in parallel always decreases, the equivalent resistance of a circuit portion.
(c) For any network constructed from four identical resistors, give a logical argument that shows the equivalent resistance cannot be exactly 2R. Your reasoning should consider all possible ways the resistors might first be grouped into sub-combinations and then combined to form the final network.