If L and R are represented as the inductance and resistance...

If $L$ and $R$ are represented as the inductance and resistance respectively then the dimensional formula of $R /$ will be $\ldots \ldots$ (a) $\mathrm{M}^{-2} \mathrm{~L}^{1} \mathrm{~T}^{-2} \mathrm{~A}^{1}$ (b) $\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1} \mathrm{~A}^{0}$ (c) $\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{0} \mathrm{~A}^{1}$ (d) $\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{1} \mathrm{~A}^{0}$

If $L$ and $R$ are represented as the inductance and resistance respectively then the dimensional formula of $R /$ will be $\ldots \ldots$
(a) $\mathrm{M}^{-2} \mathrm{~L}^{1} \mathrm{~T}^{-2} \mathrm{~A}^{1}$
(b) $\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1} \mathrm{~A}^{0}$
(c) $\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{0} \mathrm{~A}^{1}$
(d) $\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{1} \mathrm{~A}^{0}$

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Key Concepts

Dimensional Analysis

Dimensional analysis is a method used to express physical quantities in terms of basic dimensions such as mass, length, time, and electric current. It is a powerful technique to check the consistency of equations and to deduce relationships between physical quantities by comparing their dimensions.

Dimensions of Electrical Quantities

Electric quantities such as resistance and inductance have specific dimensions derived from their definitions in physical laws. For example, resistance is defined via Ohm’s law and represents the ratio of voltage to current, while inductance relates magnetic flux to current. Understanding these dimensions is essential in performing calculations and converting between units.

Ratio of Derived Quantities

When one calculates the ratio between two derived physical quantities, their dimensional formulas can be combined or reduced by dividing one by the other. This operation can lead to a simplification where many fundamental dimensions cancel out, ultimately resulting in a new dimension that characterizes the ratio, such as a time inverse in certain circuit relations.

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