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

Two solenoids $A$ and $B$ of equal number of turns have their lengths and radii in the same ratio $1 : 3$. The ratio of the self-inductance of solenoid $A$ to that of $B$ will be

When the number of turns and the length of the solenoid are doubled keeping the area of cross-section same, the inductance

The dimensional formula of self-inductance is . . . . . . .

$A$ current $I$ produces a magnetic flux $\phi$ per turn in a coil of $n$ turns. The self-inductance of the coil is $L$. The relation between them is:

$A$ graph of magnetic flux $(\phi)$ versus current $(I)$ is shown for $4$ different inductors $P, Q, R, S$. The minimum value of inductance is for inductor:

Vedclass Test Series

Exam Paper Generator

Online Exam Module