If cell constant doubles and resistance of cell is halved, what will be new resistivity?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → resistivity becomes 1/4 times
Resistance, resistivity and cell constant (G* = l/A) are related by:
R = ρ × (l/A) = ρG* ⇒ ρ = R/G*
With the cell constant doubled and the resistance halved:
ρ′ = (R/2)/(2G*) = (1/4)(R/G*) = ρ/4
The resistivity becomes one-fourth of its earlier value.
Why the other options are incorrect
Option (1) resistivity becomes 4 times — Incorrect. Four times is the change in conductivity, κ = G*/R, not in resistivity.
Option (3) resistivity remains same — Incorrect. This comes from writing ρ = R × G* (2 × ½ = 1) instead of ρ = R/G*.
Option (4) resistivity does not depend on cell constant — Incorrect. The question treats ρ as worked out from the measured resistance by ρ = R/G*, so the cell constant enters the value.