Question

The dimensions of self-inductance $L$ are

• A. $[ML^2T^{−2}A^{−2}]$
• B. $[ML^2T^{−1}A^{−2}]$
• C. $[ML^2T^{−1}A^{−1}]$
• D. $[ML^{-2}T^{−2}A^{−2}]$

Answer 1

Answer: (A)

Self-inductance $L=\frac{e}{\Delta i / \Delta t}=\frac{e \Delta t}{\Delta i}$
$\therefore $ Unit of $L=\frac{\text { Volt -second }}{\text { Ampere }}$
$=\frac{(\text { Joule } / \text { Coulomb }) \text { second }}{\text { Ampere }}$
$=\frac{\text { Newton-metre-second }}{\text { Coulomb-ampere }}$
$\Rightarrow $ Unit of $L =\frac{\text { Newton-metre }}{\text { Ampere }^{2}}$
$\therefore [ L ] =\frac{\left[ ML T^{2}\right][ L ]}{\left[ A ^{2}\right]}=\left[ ML ^{2} T ^{-2} A ^{-2}\right]$