Question

The dimensions of ‘self-inductance’ are:

• A. \( [MLT^{-2}A^{-2}] \)
• B. \( [ML^2T^{-1}A^{-1}] \)
• C. \( [ML^{-1}T^{-2}A^{-2}] \)
• D. \( [ML^2T^{-2}A^{-2}] \)

Hint:

Use dimensional analysis on the formula \( V = L \frac{dI}{dt} \) to find dimensions of self-inductance: \( L = \frac{V}{\frac{dI}{dt}} \).

Answer 1

The Correct Option is D

Self-inductance \( L \) is defined from the formula: \[ V = L \cdot \frac{dI}{dt} \Rightarrow L = \frac{V}{\frac{dI}{dt}} = \frac{ML^2T^{-3}A^{-1}}{A T^{-1}} = [ML^2T^{-2}A^{-2}] \] Where: - \( V \): potential difference → \( [ML^2T^{-3}A^{-1}] \) - \( \frac{dI}{dt} \): rate of change of current → \( [AT^{-1}] \) % Final Answer Statement Answer: \( \boxed{\text{(D)} \ [ML^2T^{-2}A^{-2}]} \)