A) its length
B) the number of turns
C) the resistance of the coil
D) the square of the number of turns
Correct Answer: D
Solution :
From the relation, \[L={{\mu }_{0}}{{n}^{2}}l\,A\] \[\Rightarrow \] \[L={{\mu }_{0}}\frac{{{N}^{2}}}{l}A\] \[\left( \because \,n=\frac{N}{l} \right)\] \[\Rightarrow \] \[L\propto {{N}^{2}}\] Thus, inductance of a coil is directly proportional to square of number of turns.
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