Dimensional formula of self inductance is

Question

Dimensional formula of self inductance is (A) [MLT-2A-2] (B) [ML2T-1A-2] (C) [ML2T-2A-2] (D) [ML2T-2A-1]

Tardigrade Admin · Accepted Answer

Induced emf |ε |=L(dI/dt) where L is the self inductance and (dI/dt) is the rate of change of current. ∴ Dimensional formula of L=(|ε |/(dI)dt) =([ML2T-3A-1]/[AT-1]) =[ML2A-2T-2]

Q. Dimensional formula of self inductance is

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

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

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

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

Induced emf $∣ ε ∣ = L \frac{d I}{d t}$
where $L$ is the self inductance and $\frac{d I}{d t}$ is the rate of change of current.
$∴$ Dimensional formula of $L = \frac{∣ ε ∣}{\frac{d I}{d t}}$
$= \frac{[ M L ^{2} T ^{- 3} A ^{- 1} ]}{[ A T ^{- 1} ]}$
$= [M L^{2} A^{- 2} T^{- 2}]$

Q. Dimensional formula of self inductance is

[MLT−2A−2]

[ML2T−1A−2]

[ML2T−2A−2]

[ML2T−2A−1]

Induced emf ∣ε∣=LdtdI​ where L is the self inductance and dtdI​ is the rate of change of current. ∴ Dimensional formula of L=dtdI​∣ε∣​ =[AT−1][ML2T−3A−1]​ =[ML2A−2T−2]

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

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

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

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

Induced emf $∣ ε ∣ = L \frac{d I}{d t}$
where $L$ is the self inductance and $\frac{d I}{d t}$ is the rate of change of current.
$∴$ Dimensional formula of $L = \frac{∣ ε ∣}{\frac{d I}{d t}}$
$= \frac{[ M L ^{2} T ^{- 3} A ^{- 1} ]}{[ A T ^{- 1} ]}$
$= [M L^{2} A^{- 2} T^{- 2}]$