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 _________.
$L, C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $M L^2 T^{-4} A^{-2}$ corresponds to _________.
Updated On: Apr 12, 2026
- $\frac{R}{\sqrt{LC}}$
- $\frac{R}{LC}$
- $\frac{C}{\sqrt{LR}}$
- $\frac{1}{R} \sqrt{\frac{L}{C}}$
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
We need to find which combination of circuit components matches the given dimensional formula.
Step 2: Key Formula or Approach:
Know the base dimensions:
$R = [M L^2 T^{-3} A^{-2}]$
$\sqrt{LC} = [T]$ (Time constant or period property)
$LC = [T^2]$
Step 3: Detailed Explanation:
Let's analyze option (A): $\frac{R}{\sqrt{LC}}$.
Dimensions of Resistance $R$:
From $P = I^2 R \implies R = \frac{Power}{I^2} = \frac{[M L^2 T^{-3}]}{[A^2]} = [M L^2 T^{-3} A^{-2}]$.
Dimensions of $\sqrt{LC}$:
We know resonance frequency $\omega = \frac{1}{\sqrt{LC}}$.
So, $[\frac{1}{\sqrt{LC}}] = [\omega] = [T^{-1}] \implies [\sqrt{LC}] = [T]$.
Now, dimensions of $\frac{R}{\sqrt{LC}}$:
$[ \frac{M L^2 T^{-3} A^{-2}}{T} ] = [M L^2 T^{-4} A^{-2}]$.
This matches the target formula exactly.
Step 4: Final Answer:
The formula corresponds to $\frac{R}{\sqrt{LC}}$.
We need to find which combination of circuit components matches the given dimensional formula.
Step 2: Key Formula or Approach:
Know the base dimensions:
$R = [M L^2 T^{-3} A^{-2}]$
$\sqrt{LC} = [T]$ (Time constant or period property)
$LC = [T^2]$
Step 3: Detailed Explanation:
Let's analyze option (A): $\frac{R}{\sqrt{LC}}$.
Dimensions of Resistance $R$:
From $P = I^2 R \implies R = \frac{Power}{I^2} = \frac{[M L^2 T^{-3}]}{[A^2]} = [M L^2 T^{-3} A^{-2}]$.
Dimensions of $\sqrt{LC}$:
We know resonance frequency $\omega = \frac{1}{\sqrt{LC}}$.
So, $[\frac{1}{\sqrt{LC}}] = [\omega] = [T^{-1}] \implies [\sqrt{LC}] = [T]$.
Now, dimensions of $\frac{R}{\sqrt{LC}}$:
$[ \frac{M L^2 T^{-3} A^{-2}}{T} ] = [M L^2 T^{-4} A^{-2}]$.
This matches the target formula exactly.
Step 4: Final Answer:
The formula corresponds to $\frac{R}{\sqrt{LC}}$.
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