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 :

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Both Statement I and Statement II are true

Statement I is false but Statement II is true

Current Electricity PYQ — JEE Main 2023 · 15 Apr · Shift 1 · Q59 with Solution

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Correct answer: C

For resistors in series, the equivalent resistance is the sum of all resistances:

$R_{\text{eq}} = R_1 + R_2 + R_3 + \cdots$

Since all resistances are positive,

$R_{\text{eq}} > R_1,\; R_{\text{eq}} > R_2,\; \text{etc.}$

So the equivalent resistance in series is greater than the largest resistance, and certainly not smaller than the least resistance.

Hence, Statement I is false.

Resistivity $\rho$ generally depends on temperature.

For example, for conductors,

$\rho_T = \rho_0[1 + \alpha (T-T_0)]$

where $\alpha$ is the temperature coefficient of resistivity.

Thus, resistivity is not independent of temperature.

Hence, Statement II is false.

Therefore, the correct option is:

$\boxed{\text{C}}$

Stored correct answer = C

My derived answer = C

So, the answer agrees with the stored correct answer.