Wheatstone bridge principle is used to measure the specific resistance ($\mathrm{S}_{1}$) of given wire, having length L, radius r. If X is the resistance of wire, then specific resistance is: $\mathrm{S}_{1}=\mathrm{X}\left(\frac{\pi \mathrm{r}^{2}}{\mathrm{~L}}\right)$. If the length of the wire gets doubled then the value of specific resistance will be :

JEE Main · 2024 · 27 Jan 2024 · Shift 2 · Current Electricity

Wheatstone bridge principle is used to measure the specific resistance (

S_{1}

) of given wire, having length L, radius r. If X is the resistance of wire, then specific resistance is:

S_{1} = X (\frac{π r ^{2}}{L})

. If the length of the wire gets doubled then the value of specific resistance will be :

(A) $\frac{S _{1}}{4}$
(B) $2 S_{1}$
(C) $\frac{S _{1}}{2}$
(D) $S_{1}$ ✓ Correct

Answer: (D)

Solution

Specific resistance (resistivity) is an intrinsic property of the material — it depends only on the substance and its temperature, never on the wire's dimensions. If the length is doubled, the measured resistance

X

scales up in exact proportion to

L

, so the combination

X \frac{π r ^{2}}{L}

that defines

S_{1}

is unchanged. The specific resistance remains

S_{1}

JEE Main · 2024 · 27 Jan 2024 · Shift 2 · Single correct option

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JEE Main · 2024 · 27 Jan 2024 · Shift 2 · Current Electricity

Solution

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