Select the quantity whose dimensions are equal to:

ML²T^-4A^-2

Options:

• (1) R / √LC
• (2) (1/R) √(L/C)
• (3) 3R / LC
• (4) 4C / √LR

To solve this question, we must compare the dimensions of each option with the required dimensions:

ML²T^-4A^-2

First, let us recall the dimensions of the electrical quantities involved.

Resistance:

[R] = ML²T^-3A^-2

Inductance:

[L] = ML²T^-2A^-2

Capacitance:

[C] = M^-1L^-2T⁴A²

Now calculate:

LC = T²

Therefore:

√LC = T

For option (1):

R / √LC

Dimensions become:

(ML²T^-3A^-2) / T

= ML²T^-4A^-2

This exactly matches the required dimensions.

Dimensional analysis is an important tool in physics because it helps verify equations and identify correct formulas without performing lengthy calculations. In electrical circuits, resistance, inductance, and capacitance often appear together, and understanding their dimensions makes it easier to solve problems related to AC circuits, resonance, and electromagnetic phenomena.

Hence, the correct quantity is:

R / √LC