The dimension of mutual inductance is (Denote dimension of current as A)

Question

The dimension of mutual inductance is (Denote dimension of current as A) (A) ML2 T2 A-2 (B) ML2 T-2 A-2 (C) ML-2 T2 A-2 (D) ML-2 T-3 A-1

Tardigrade Admin · Accepted Answer

As we know, induced operatornameEmf=L × (Δ I/Δ t) ⇒ [ L ] =([ text Voltage ][ T ]/[ text Current ])=([ ML 2 T -3 A -1][ T ]/[ A ]) =[ M L 2 T -2 A -2] ∴ Dimension of mutual inductance is [M L2 T-2 A-2]

Q. The dimension of mutual inductance is (Denote dimension of current as A)

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

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

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

$M L^{- 2} T^{- 3} A^{- 1}$

$M L^{2} T^{- 3} A^{- 3}$

As we know, induced $Emf = L \times \frac{Δ I}{Δ t}$
$\Rightarrow [L] = \frac{[ Voltage ] [ T ]}{[ Current ]} = \frac{[ M L ^{2} T ^{- 3} A ^{- 1} ] [ T ]}{[ A ]}$
$= [M L^{2} T^{- 2} A^{- 2}]$
$∴$ Dimension of mutual inductance is
$[M L^{2} T^{- 2} A^{- 2}]$

Q. The dimension of mutual inductance is (Denote dimension of current as A)

ML2T2A−2

ML2T−2A−2

ML−2T2A−2

ML−2T−3A−1

ML2T−3A−3