Four 12 Ω resistors are connected together. Which of the following resistances cannot be formed using all 4 resistors?
A) 48 Ω
B) 9.0 Ω
C) 12 Ω
D) 60 Ω
E) 20 Ω

Question

Quizplus · Accepted Answer

To find the possible resistances that can be formed, we can combine the resistors in different ways:
- Connecting all four resistors in series: this gives a total resistance of 48 Ω (12+12+12+12)
- Connecting all four resistors in parallel: this gives a total resistance of 3 Ω (1/12 + 1/12 + 1/12 + 1/12)^-1
- Connecting two resistors in series and then connecting the pairs in parallel: this gives a total resistance of 6 Ω ((12+12) || (12+12))
- Connecting two resistors in parallel and then connecting the pairs in series: this gives a total resistance of 24 Ω ((12 || 12) + (12 || 12))
Therefore, the only resistance that cannot be formed using all four resistors is 60 Ω.

Four 12 Ω Resistors Are Connected Together