The dimensions of self-inductance L are

Question

The dimensions of self-inductance L are (A) [ML2T−2A−2] (B) [ML2T−1A−2] (C) [ML2T−1A−1] (D) [ML-2T−2A−2]

Tardigrade Admin · Accepted Answer

Self-inductance L=(e/Δ i / Δ t)=(e Δ t/Δ i) ∴ Unit of L=( text Volt -second / text Ampere ) =(( text Joule / text Coulomb ) text second / text Ampere ) =( text Newton-metre-second / text Coulomb-ampere ) ⇒ Unit of L =( text Newton-metre / text Ampere 2) ∴ [ L ] =([ ML T2][ L ]/[ A 2])=[ ML 2 T -2 A -2]

Q. The dimensions of self-inductance $L$ are

$[M L^{2} T^{- 2} A^{- 2}]$

$[M L^{2} T^{- 1} A^{- 2}]$

$[M L^{2} T^{- 1} A^{- 1}]$

$[M L^{- 2} T^{- 2} A^{- 2}]$

Q. The dimensions of self-inductance L are

[ML2T−2A−2]

[ML2T−1A−2]

[ML2T−1A−1]

[ML−2T−2A−2]

Self-inductance L=Δi/Δte​=ΔieΔt​ ∴ Unit of L= Ampere Volt -second ​ = Ampere ( Joule / Coulomb ) second ​ = Coulomb-ampere Newton-metre-second ​ ⇒ Unit of L= Ampere 2 Newton-metre ​ ∴[L]=[A2][MLT2][L]​=[ML2T−2A−2]

Q. The dimensions of self-inductance $L$ are

$[M L^{2} T^{- 2} A^{- 2}]$

$[M L^{2} T^{- 1} A^{- 2}]$

$[M L^{2} T^{- 1} A^{- 1}]$

$[M L^{- 2} T^{- 2} A^{- 2}]$