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MCQEasyJEE 2023Combination of Resistors

JEE Physics 2023 Question with Solution

Given below are two statements:

Statement I : The equivalent resistance of resistors in a series combination is smaller than the 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

    Both Statement I and Statement II are true

  • B

    Both Statement I and Statement II are false

  • C

    Statement I is true but Statement II is false

  • D

    Statement I is false but Statement II is true

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Two statements about equivalent resistance and resistivity.

Find: Which option correctly identifies the truth values of Statement I and Statement II.

For resistors connected in series, the equivalent resistance is

Req=R1+R2+R3+⋯R_{eq} = R_1 + R_2 + R_3 + \cdots

This sum is always greater than each individual resistance. Therefore, the equivalent resistance cannot be smaller than the least resistance in the series. So, Statement I is false.

The resistivity of a material generally depends on temperature. For most conductors, resistivity increases with temperature, while for semiconductors it usually decreases with temperature. Therefore, resistivity is not independent of temperature. So, Statement II is false.

Hence, both Statement I and Statement II are false. The correct option is B.

Common mistakes

  • Assuming series combination reduces resistance. This is wrong because in series, resistances add directly, so the equivalent resistance becomes larger, not smaller. Use Req=R1+R2+⋯R_{eq} = R_1 + R_2 + \cdots.

  • Confusing resistivity with a fixed material constant under all conditions. This is wrong because resistivity changes with temperature. Treat resistivity as a temperature-dependent property unless stated otherwise.

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