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Match the following two columns. {:(,"...

Match the following two columns.
`{:(,"Column I",,"Column II"),("A.","Electrical resistance",1.,["ML"^(3)"T"^(-3)"A"^(-2)]),("B.","Electrical potential",2.,["ML"^(2)"T"^(-3)"A"^(-2)]),("C.","Specific resistance",3.,["ML"^(2)"T"^(-3)"A"^(-1)]),("D.","Specific conductance",4.,"None"):}`

A

A-2, B-3, C-1, D-4

B

A-2, B-4, C-3, D-1

C

A-1, B-2, C-4, D-3

D

A-1, B-3, C-2, D-4

Text Solution

Verified by Experts

The correct Answer is:
A
The dimensions of electrical resistance
`R=(V)/(I)=(((W)/(q)))/(I)=((W)/(It))/((I)`
`(W)/(I^(2)t)=["ML"^(2)"T"^(-2)"T"^(-1)"A"^(-2)]=["ML"^(2)"T"^(-3)"A"^(-2)]`
Then, (A) `to` (2)
The dimensions of electrical potential
`V=(W)/(q)=(W)/(It)=["ML"^(2)"T"^(-2)"A"^(-1)"T"^(-1)]=["ML"^(3)"T"^(-3)"A"^(-2)]`
Then , (B) `to` (3)
The dimensions of specific resistance
`rho=R(l)/(A)=["ML"^(2)"T"^(-3)"A"^(-2)]["L"]=["ML"^(3)"T"^(-3)"A"^(-2)]`
Thus, (C) `to` (1) and the dimensions of specific conductance
`sigma=(1)/(rho)=(1)/(["ML"^(3)"T"^(-3)"A"^(-2)])=["M"^(-1)"L"^(-3)"T"^(3)"A"^(2)]`
=not given in column
Thus, (D)`to`(4)
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