A coil is wound as a transformer of rectangular cross-section. If… - Vidyadip

MCQ

A coil is wound as a transformer of rectangular cross-section. If all the linear dimensions of the transformer are increased by a factor $2$ and the number of turns per unit length of the coil remain the same, the self inductance increased by a factor of

A
$16$
B
$12$
✓
$8$
D
$4$

✓

Answer

Correct option: C.

$8$

c
(c) Self inductance $L = {\mu _0}{N^2}A\, /l = {\mu _0}{n^2}lA$
Where $n$ is the number of turns per unit length and $N$ is the total number of turns and $N = nl$
In the given question n is same. $A$ is increased $4$ times and $l$ is increased $2$ times and hence $L$ will be increased $8$ times.

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