Question

ASSERTION
The dimensional formula for product of resistance and conductance is same as for dielectric constant
REASON
Both have dimensions of time constant
(A) Both Assertion and Reason are correct, and Reason is the correct explanation for Assertion
(B) Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
(C) Assertion is correct but Reason is incorrect
(D) Both Assertion and Reason are incorrect

Answer 1

Hint:Conductance is just the opposite of resistance. Use this statement to equate and find the answer. Therefore, the dimension of Conductance is just the opposite of resistance. The dimension for Dielectric constant has no value and so it is equal to 1.

Complete step by step answer:
We know that Resistance is R.
And Conductance is \[\dfrac{1}{R}\].
Now by multiplying resistance and conductance we get,
\[Resistance\,\, \times {\text{ }}conductance\]
\[R \times \dfrac{1}{R}\]
Now write the dimensions of R is \[\left[ {M{L^2}{A^{ - 2}}{T^{ - 3}}} \right]\]and dimensions of conductance is \[\dfrac{1}{{\left[ {M{L^2}{A^{ - 2}}{T^{ - 3}}} \right]}}\] since resistance is \[\dfrac{1}{{conduc\tan ce}}\].
Then, \[\left( {{M^0}{L^0}{T^0}} \right) = 1\]
the dielectric constant is dimensionless
Therefore, the correct option is c).
Additional information:
Resistance is the opposition that a substance offers to the flow of electric current. It is represented by the uppercase letter R. The standard unit of resistance is the ohm, sometimes written out as a word, and sometimes symbolized by the uppercase Greek letter omega: Conductance is the measure of how easily electricity flows along a certain path through an electrical element, and since electricity is so often explained in terms of opposites, conductance is considered the opposite of resistance. In terms of resistance and conductance, the reciprocal relationship between the two can be expressed through the following equation: R = 1/G, G=1/R, where R equals resistance and G equals conduction.

Note: Students need to be familiar with the concepts of resistance, conductance, and dielectric constant to be able to solve the sum. Students need to know that Dielectric constant is a ratio and therefore it has no value and is equal to 1.