JEE Main 2023 · 15 April · morning · Single correct · +4 / −1
Given below are two statements:
Statement I : The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination.
Statement II : The resistivity of the material is independent of temperature.
In the light of the above statements, choose the correct answer from the options given below :
- (a) Statement I is true but Statement II is false
- (b) Both Statement I and Statement II are true
- (c) Both Statement I and Statement II are false
- (d) Statement I is false but Statement II is true
Answer and solution
Answer (c) Both Statement I and Statement II are false
Solution
Physics sir · 3 steps
Check each statement against one formula: series adds resistances, and resistivity moves with temperature.
- Statement I. In series, resistances add: Rₛ = R₁ + R₂ + …. Every term is positive, so the sum is larger than even the largest resistor, never smaller than the least one. Statement I is false.
ρ_T = ρ₀[1 + α(T - T₀)]
- Statement II. Resistivity depends on temperature through the coefficient α. For a metal α > 0, so ρ rises as it heats up. For a semiconductor it falls. Statement II is false.
- So. Both statements are false, which is option (c).
The idea to keep. Series gives more than the largest resistor, parallel gives less than the smallest. Resistivity is a material property that changes with temperature. Only its dependence on length and area is absent.
Answer from the NTA final answer key. Solution by PrepWiser.