Case: Read the passage and answer the question.
Consider two long co-axial solenoids, each of length l. We denote the radius of the inner solenoid S1 by \( r_1 \) and its number of turns per unit length by \( n_1 \). The corresponding quantities for the outer solenoid S2 are \( r_2 \) and \( n_2 \), respectively. Let \( N_1 \) and \( N_2 \) be the total numbers of turns of coils S1 and S2, respectively.
The dimensions of inductance are
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( [\mathrm{ML^2T^{-2}A^{-2}}] \)
The energy needed to build up a current \( I \) in an inductor is \( W=\frac{1}{2}LI^{2} \). So \( L=2W/I^{2} \) has the dimensions of energy divided by the square of current. The number 2 has no dimensions.
\( \begin{aligned} [L] &= \frac{[W]}{[I]^{2}} \\ &= \frac{[\mathrm{ML^{2}T^{-2}}]}{[\mathrm{A}]^{2}} \\ &= [\mathrm{ML^2T^{-2}A^{-2}}] \end{aligned} \)
NCERT (2026-27):
Inductance – “Inductance is a scalar quantity. It has the dimensions of [M L2 T–2 A–2] given by the dimensions of flux divided by the dimensions of current.”