L, C and R represents physical quantities inductance capacitance and resistance respectively. The dimensional formula corresponds to [2026]

Question

L, C and R represents physical quantities inductance capacitance and resistance respectively. The dimensional formula $M L^{2} T^{- 4} A^{- 2}$ corresponds to ______. [2026]

Smart Achievers · Accepted Answer

(1)

$R = \frac{V}{I} = \frac{W}{q I} = \frac{[M L^{2} T^{- 2}]}{[A^{2} T]} = [M L^{2} T^{- 3} A^{- 2}]$

$U = \frac{1}{2} L I^{2} \Rightarrow [M L^{2} T^{- 2}] = [L] [A^{2}]$

$[L] = [M L^{2} T^{- 2} A^{- 2}]$

$Q = C V \Rightarrow [A T] = [C] [M L^{2} T^{- 3} A^{- 1}]$

$[C] = [M^{- 1} L^{- 2} T^{4} A^{2}]$

$[L C] = [M L^{2} T^{- 2} A^{- 2}] \times [M^{- 1} L^{- 2} T^{4} A^{2}] = [T^{2}]$

$\frac{R}{\sqrt{L C}} = \frac{[M L^{2} T^{- 3} A^{- 2}]}{[T]} = [M L^{2} T^{- 4} A^{- 2}]$

Solution

Q.
L, C and R represents physical quantities inductance capacitance and resistance respectively. The dimensional formula $M L^{2} T^{- 4} A^{- 2}$ corresponds to ______. [2026]

1 $\frac{R}{\sqrt{L C}}$

2 $\frac{R}{L C}$

3 $\frac{C}{\sqrt{L R}}$

4 $\frac{1}{R} \sqrt{\frac{L}{C}}$

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Solution

Q. L, C and R represents physical quantities inductance capacitance and resistance respectively. The dimensional formula ML2T-4A-2 corresponds to ______. [2026]

1 RLC

2 RLC

3 CLR

4 1RLC