A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil :

a. |
Decreases by a factor of 9 |
b. |
Increases by a factor of 3 |

c. |
Decreases by a factor of 9 |
d. |
Increases by a factor of 27 |

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil :

a. |
Decreases by a factor of 9 |
b. |
Increases by a factor of 3 |

c. |
Decreases by a factor of 9 |
d. |
Increases by a factor of 27 |

1 Answer

127 votes

Total length L will remain constant

L = (3a) N (N = total turns)

and length of winding = (d) N (d = diameter of wire)

self inductance = n^{2}A

= n^{2}dN

^{ }a^{2} N ^{ }a

So self inductance will become 3 times

127 votes

127