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Chapter 12: Problem 1834

Match the following two columns. Column I \(\quad\) Column II (a) Electrical resistance (p) \(\left[\mathrm{MLT}^{-2} \mathrm{~A}^{2}\right]\) (b) Electric potential (q) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) (c) Specific resistance (r) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\) (d) Specific conductance (s) None of there (A) \(a-q, b-s, c-r, d-p\) (B) \(a-q, b-r, c-s, d-s\) (C) \(a-p, b-q, c-s, d-r\) (D) \(a-p, b-r, c-q, d-s\)

Short Answer

Expert verified
The correct matches are: (a) Electrical Resistance - q (Dimensions: \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\)) (b) Electric Potential - r (Dimensions: \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\)) (c) Specific resistance - None of these (Dimensions: \(\left[\mathrm{ML}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\)) (d) Specific conductance - p (Dimensions: \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{3} \mathrm{~A}^{2}\right]\)) The correct answer is (A) \(a-q, b-s, c-r, d-p\).

Step by step solution

01

Identify the formulas and dimensions of the given variables.

We first need to know the formulas and dimensions of the given variables: (a) Electrical resistance (R) - \(R = \frac{V}{I}\) (Ohm's Law) Dimensions of R - \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) (b) Electric potential (V) - \(V = \frac{W}{q}\) (Work per unit charge) Dimensions of V - \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\) (c) Specific resistance (ρ) - \(\rho = \frac{R}{A}\) Dimensions of ρ - \(\left[\mathrm{ML}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\) (d) Specific conductance (σ) - σ = 1/ρ Dimensions of σ - \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{3} \mathrm{~A}^{2}\right]\)
02

Match the dimensions from the two columns.

Now we can match the dimensions to the given options: (a) Electrical Resistance - q (Dimensions: \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\)) (b) Electric Potential - r (Dimensions: \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\)) (c) Specific resistance - None of these (Dimensions: \(\left[\mathrm{ML}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]\)) (d) Specific conductance - p (Dimensions: \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{3} \mathrm{~A}^{2}\right]\))
03

Identify the correct answer option.

The correct matches are: \( a-q, b-r, c-s, d-p\) This corresponds to option (A). So, the correct answer is: (A) \(a-q, b-s, c-r, d-p\)

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