A coil is wound on a core of rectangular cros | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The self-inductance $L$ of a solenoid is given by the formula $L = \mu_0 n^2 A l$,where $n$ is the number of turns per unit length,$A$ is the cros

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(C) The self-inductance $L$ of a solenoid is given by the formula $L = \mu_0 n^2 A l$,where $n$ is the number of turns per unit length,$A$ is the cross-sectional area,and $l$ is the length of the coil.Given that all linear dimensions are increased by a factor of $k = 3$:$1$. The length $l$ becomes $l' = kl = 3l$.$2$. Since the cross-section is rectangular,if its sides are $a$ and $b$,the area $A = ab$. When dimensions are scaled by $k$,the new area $A' = (ka)(kb) = k^2 A = 3^2 A = 9A$.$3$. The number of turns per unit length $n$ remains constant.Substituting these into the formula for the new inductance $L'$:$L' = \mu_0 n^2 A' l' = \mu_0 n^2 (k^2 A) (kl) = k^3 (\mu_0 n^2 A l) = k^3 L$.Substituting $k = 3$:$L' = 3^3 L = 27L$.Therefore,the self-inductance increases by a factor of $27$.

$A$ coil is wound on a core of rectangular cross-section. If all the linear dimensions of the core are increased by a factor of $3$ and the number of turns per unit length of the coil remains the same,the self-inductance increases by a factor of:

Similar Questions

$A$ coil of self-inductance $L$ is connected in series with a bulb and an a.c. source. Brightness of the bulb decreases when

The self-inductance of a solenoid is:

Define inductance, give its units and write factors on which its value depends.

The self-inductance of a coil is $L$. Keeping the length and area the same,the number of turns in the coil is increased to four times. The self-inductance of the coil will now be

Consider a long solenoid of length $l$ and radius $r$. If $n$ is the number of turns per unit length and $\mu_0$ is the permeability of free space, the inductance of the solenoid is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module