JEE PYQ: Electromagnetic Induction Question 24
Question 24 - 2019 (11 Jan Shift 2)
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:
(1) decreases by a factor of 9
(2) increases by a factor of 27
(3) increases by a factor of 3
(4) decreases by a factor of $9\sqrt{3}$
Show Answer
Answer: (3)
Solution
Total length of wire $L = (3a)N$ remains constant. Length of winding $= (d)N$ where $d$ is diameter of wire. Self inductance $= \mu_0 n^2 A l$. Since $N \propto \frac{1}{a}$ (as total wire is fixed and perimeter increases), and $A \propto a^2$: self inductance $\propto a^2 N \propto a$. When $a$ increases to $3a$, self inductance becomes 3 times.
BETA
