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Standard X

Physics

Resistivity

Match the fol...

Question

Match the following two columns:
Column I Column II
(a) Electrical resistance (p) $M L^{3} T^{- 3} A^{- 2}$
(b) Electrical potential (q) $M L^{2} T^{- 3} A^{- 2}$
(c) Specific resistance (r) $M L^{2} T^{- 3} A^{- 1}$
(d) Specific conductance (s) None of these

a - q

b - s

c - r

d - p

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a - q

b - r

c - p

d - s

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a - p

b - q

c - s

d - r

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a - p

b - r

c - q

d - s

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Solution

The correct option is D $a - q$ , $b - r$ , $c - p$ , $d - s$
(b) :
Electric potential $V = \frac{W}{q}$
So dimensions of electric potential $[V] = \frac{[M L^{2} T^{- 2}]}{[A T]} = [M L^{2} T^{- 3} A^{- 1}]$
(a) :
Electric resistance $R = \frac{V}{I}$
So dimensions of electric resistance $[R] = \frac{[M L^{2} T^{- 3} A^{- 1}]}{[A]} = [M L^{2} T^{- 3} A^{- 2}]$
(c) :
Specific resistance $ρ = \frac{R A}{l}$
So dimensions of specific resistance $[ρ] = \frac{[M L^{2} T^{- 3} A^{- 2}] \times [L^{2}]}{[L]} = [M L^{3} T^{- 3} A^{- 2}]$
(d) :
Specific conductance $σ = \frac{1}{ρ}$
So dimensions of specific conductance $[σ] = [M^{- 1} L^{- 3} T^{3} A^{2}]$
Option B is correct.

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Column I	Column II
(a) Electrical resistance	(p) $M L^{3} T^{- 3} A^{- 2}$
(b) Electrical potential	(q) $M L^{2} T^{- 3} A^{- 2}$
(c) Specific resistance	(r) $M L^{2} T^{- 3} A^{- 1}$
(d) Specific conductance	(s) None of these

Match the following two columns:Column IColumn II(a) Electrical resistance(p) ML3T−3A−2(b) Electrical potential(q) ML2T−3A−2(c) Specific resistance(r) ML2T−3A−1(d) Specific conductance(s) None of these

Match the following two columns:
Column I Column II
(a) Electrical resistance (p) $M L^{3} T^{- 3} A^{- 2}$
(b) Electrical potential (q) $M L^{2} T^{- 3} A^{- 2}$
(c) Specific resistance (r) $M L^{2} T^{- 3} A^{- 1}$
(d) Specific conductance (s) None of these