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AIIMS 2001
Exam
AIIMS
Year
2001
Subject
Physics
Chapter
Units and Dimensions

AIIMS 2001 · Physics · Units and Dimensions

Dimension of resistivity is

Dimension of resistivity is

Options

  1. AML2 T−2 A−1\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-1}
  2. BML3 T−3 A−2\mathrm{ML}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-2}
  3. CML3 T−2 A−1\mathrm{ML}^3 \mathrm{~T}^{-2} \mathrm{~A}^{-1}
  4. DML2 T−2 A−2\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-2}.

Correct answer

C. ML3 T−2 A−1\mathrm{ML}^3 \mathrm{~T}^{-2} \mathrm{~A}^{-1}

Step-by-step solution

By definition R=ρlA⇒ρ=RAl=VIAl=VAIl∴[ρ]=[V][A][I][l]=ML2 T−2 L2AL2=[ML3 T−2 A−1]\begin{aligned}R & =\rho \frac{l}{A}\\ \Rightarrow \quad \rho & =\frac{R A}{l}=\frac{\frac{V}{I} A}{l}=\frac{V A}{I l}\\ \therefore \quad[\rho] & =\frac{[V][A]}{[I][l]}\\ & =\frac{\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~L}^2}{\mathrm{AL}^2}=\left[\mathrm{ML}^3 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right] \end{aligned}
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