We want to design a carbon resistor in shape of a cylinder. Its resistivity is known precisely. The diameter is measured by a screw gauge whose main scale has a least count of 1 mm and circular scale has 100 divisions. The length is measured by a vernier callipers whose main scale is 1 mm and 9 main scale divisions coincide with 10 vernier scale divisions. We wish that the fourth band in the colour code be painted gold. In which of the following screw gauge readings and vernier callipers readings will our goal be achieved?
Select all that apply

Question

We want to design a carbon resistor in shape of a cylinder. Its resistivity is known precisely. The diameter is measured by a screw gauge whose main scale has a least count of 1 mm and circular scale has 100 divisions. The length is measured by a vernier callipers whose main scale is 1 mm and 9 main scale divisions coincide with 10 vernier scale divisions. We wish that the fourth band in the colour code be painted gold. In which of the following screw gauge readings and vernier callipers readings will our goal be achieved?

Select all that apply

G1 Physics · Accepted Answer

Gold tolerance band means the relative measurement uncertainty in resistance must be within 5%. Since R=ρL/A ∝ L/d², percentage error ≈ percentage error in L + 2 percentage error in d. Evaluating the listed instrument readings, only B and C satisfy the 5% requirement. Correct answers: B,C.