Question:
If \(L, C\) and \(R\) denote the inductance, capacitance and resistance respectively, the dimensional formula for \(C^2LR\) is
If \(L, C\) and \(R\) denote the inductance, capacitance and resistance respectively, the dimensional formula for \(C^2LR\) is
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Always write full dimensional formulas before simplifying.
Updated On: Apr 23, 2026
- \([ML^{-2}T^{0}]\)
- \([M^{0}L^{0}T^{3}]\)
- \([M^{-1}L^{-2}T^{6}]\)
- \([M^{0}T^{2}]\)
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The Correct Option is B
Solution and Explanation
Concept:
\[
[L] = [M L^2 T^{-2} A^{-2}],\quad
[C] = [M^{-1} L^{-2} T^4 A^2],\quad
[R] = [M L^2 T^{-3} A^{-2}]
\]
Step 1: Compute \(C^2\).
\[ C^2 = [M^{-2} L^{-4} T^8 A^4] \]
Step 2: Multiply all.
\[ C^2LR = [M^{-2} L^{-4} T^8 A^4] \times [M L^2 T^{-2} A^{-2}] \times [M L^2 T^{-3} A^{-2}] \]
Step 3: Combine powers.
\[ M^{-2+1+1} = M^0 \] \[ L^{-4+2+2} = L^0 \] \[ T^{8-2-3} = T^3 \] \[ A^{4-2-2} = A^0 \] \[ = [M^0 L^0 T^3] \] Conclusion: \[ {[M^0 L^0 T^3]} \]
Step 1: Compute \(C^2\).
\[ C^2 = [M^{-2} L^{-4} T^8 A^4] \]
Step 2: Multiply all.
\[ C^2LR = [M^{-2} L^{-4} T^8 A^4] \times [M L^2 T^{-2} A^{-2}] \times [M L^2 T^{-3} A^{-2}] \]
Step 3: Combine powers.
\[ M^{-2+1+1} = M^0 \] \[ L^{-4+2+2} = L^0 \] \[ T^{8-2-3} = T^3 \] \[ A^{4-2-2} = A^0 \] \[ = [M^0 L^0 T^3] \] Conclusion: \[ {[M^0 L^0 T^3]} \]
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