What is the maximum number of different electrical combinations possible with three equal resistances ?

When considering three equal resistances (R), there are exactly four distinct electrical combinations possible for a two-terminal network. These are: (1) All three in series, resulting in an equivalent resistance of 3R [5]. (2) All three in parallel, resulting in R/3 [4]. (3) Two in parallel connected in series with the third, resulting in (R/2) + R = 3R/2 [3]. (4) Two in series connected in parallel with the third, resulting in (2R * R) / (2R + R) = 2R/3 [3]. These four configurations yield unique equivalent resistance values. While more complex bridge or delta-wye transformations exist for three-terminal networks, for standard two-terminal equivalent resistance problems involving identical resistors, these four represent the exhaustive set of distinct topological arrangements.

Sources

1. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > 11.6 RESISTANCE OF A SYSTEM OF RESISTORS > p. 181
2. [5] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.5 > p. 183
3. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 186
4. [4] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > 11.6 RESISTANCE OF A SYSTEM OF RESISTORS > p. 182
5. [3] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > EXERCISES > p. 193