A coil is wound on a transformer core of rectangular cross-section. If all the linear dimensions of the core are increased by a factor of 2 and the number of turns per unit length of the coil remains the same, the self-inductance increases by a factor of
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 8
A long coil has \( n \) turns per unit length, cross-sectional area \( A \) and length \( l \). When it is wound on a core of relative permeability \( \mu_r \), its self-inductance is \( L=\mu_r\mu_0n^{2}Al \). With the same core material and the same \( n \), \( L\propto Al \).
When every linear dimension of the core is doubled, the area and the length become:
\( \begin{aligned} A' &= 2^{2}A \\ &= 4A \end{aligned} \)
\( l'=2l \)
The new self-inductance compared with the old one is:
\( \begin{aligned} \frac{L'}{L} &= \frac{A'l'}{Al} \\ &= \frac{4A\times2l}{Al} \\ &= 8 \end{aligned} \)
NCERT (2026-27):
Summary – “8. The self-inductance of a long solenoid, the core of which consists of a magnetic material of relative permeability μr, is given by
\( L=\mu_r\mu_0n^{2}Al \)
where A is the area of cross-section of the solenoid, l its length and n the number of turns per unit length.”