The physical quantities L, C and R represent inductance, capacitance and resistance, respectively. Which of the following expressions has the dimensional formula [M L² T⁻⁴ A⁻²]?
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Question

The physical quantities L, C and R represent inductance, capacitance and resistance, respectively. Which of the following expressions has the dimensional formula [M L² T⁻⁴ A⁻²]?

G1 Physics · Accepted Answer

The dimensions of resistance are [R] = M L² T⁻³ A⁻². For an inductor, U = (1 ÷ 2)LI², so [L] = M L² T⁻² A⁻². For a capacitor, Q = CV, which gives [C] = M⁻¹ L⁻² T⁴ A². Therefore, [LC] = T², so [√(LC)] = T. Hence, [R ÷ √(LC)] = M L² T⁻³ A⁻² ÷ T = M L² T⁻⁴ A⁻². Correct option: A.