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The dimensional formula of jω L is ________. Take Q as the dimension of charge.

Asked in GUJCET 2019 · Units and dimensions

• (1) M⁻¹L²T⁻¹Q⁻²
• (2) M⁻¹L⁻²T⁻¹Q⁻²
• (3) M¹L²T⁻¹Q⁻²
• (4) M¹L²T¹Q⁻²

Step-by-step solution

Why the other options are wrong

• (1) M⁻¹L²T⁻¹Q⁻² is the answer with the mass exponent reversed. A reactance is a resistance, and in R=(WT)/(Q²) the energy stands in the numerator, so M has to come out +1.
• (2) No single slip produces M⁻¹L⁻²T⁻¹Q⁻² -- it is the answer with the signs on both M and L reversed. Sanity check: ω L is a reactance, so it carries the dimensions of resistance, (WT)/(Q²)=M¹L²T⁻¹Q⁻².
• (4) M¹L²T¹Q⁻² comes from multiplying the inductance by the time instead of dividing by it: [L]=M¹L²T⁰Q⁻², so LT gives M¹L²T¹Q⁻² while L/T -- which is what ω L means, since ω=(2π)/T -- gives the answer.

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