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Question:

In an electrical circuit containing L,C and R which of the following does not denote the dimensions of the frequency ? a) LC b)1/square root of LC c) 1/RC d)R/L

Answer:

Dimension of Resistance = Potential Difference / Current = ML²T^-3A-1 / A = ML²T^-3A^-2

Dimension of Capacitance = Charge / Potential Difference = AT/ML²T^-3A^-1 = M^-1L^-2T⁴A²

Dimension of self Inductance [L]=[ϕ] / [I] = MT⁻²L²A⁻¹ / A = ML²T^-2A^-2

a) Dimension of LC = ML²T^-2A^-2* M^-1L^-2T⁴A²= T²
b) Dimension of 1/ = (ML²T^-2A^-2 * M^-1L^-2T⁴A²)^-1/2 = T^-1= 1/T
c) Dimension of 1/ RC = 1/ (ML²T^-3A^-2* M^-1L^-2T⁴A²) = 1 / T
d) Dimension of R / L = ML²T^-3A^-2/ ML²T^-2A^-2= 1/ T

So answer is (a)

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