10 resistors each of resistance 10 Ω can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be ___________.

Solution

Physics sir · 3 steps

All in series gives the biggest resistance, all in parallel the smallest; the ratio comes out as n².

1. Maximum in series. Resistances add in series, so connecting all 10 in a line gives the largest value: Rₘₐₓ = 10 × 10 = 100 Ω.
2. Minimum in parallel. In parallel the reciprocals add. For 10 equal resistors, 1/Rₘᵢₙ = 10/10, so Rₘᵢₙ = 10/10 = 1 Ω.

   Rₘₐₓ/Rₘᵢₙ = nR/(R/n) = n²

3. So. With n = 10, the ratio is (100 Ω)/(1 Ω) = 10² = 100.

The common slip: 10. Taking the parallel combination as 10 Ω instead of 10/10 = 1 Ω gives a ratio of 10, not 100.

The idea to keep. For n identical resistors, series gives nR and parallel gives R/n. Their ratio is always n², whatever the value of R.

Answer from the NTA final answer key. Solution by PrepWiser.