If N is the number of turns in a coil,the val | vedclass

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

Question

(D) The self-inductance $L$ of a coil is defined as $L = \frac{N \phi}{i}$,where $N$ is the number of turns,$\phi$ is the magnetic flux through each t

Vedclass · Accepted Answer

$N^2$

Vedclass · Answer

(D) The self-inductance $L$ of a coil is defined as $L = \frac{N \phi}{i}$,where $N$ is the number of turns,$\phi$ is the magnetic flux through each turn,and $i$ is the current.For a solenoid,the magnetic flux $\phi$ is given by $\phi = B A$,where $B$ is the magnetic field and $A$ is the cross-sectional area.The magnetic field $B$ inside a solenoid is $B = \mu_0 n i = \frac{\mu_0 N i}{l}$,where $n$ is the number of turns per unit length $(n = N/l)$ and $l$ is the length of the solenoid.Substituting $B$ into the flux equation: $\phi = \left( \frac{\mu_0 N i}{l} \right) A$.Now,substituting $\phi$ into the expression for $L$: $L = \frac{N}{i} \left( \frac{\mu_0 N i A}{l} \right) = \frac{\mu_0 N^2 A}{l}$.Thus,the self-inductance $L$ is proportional to $N^2$.

If $N$ is the number of turns in a coil,the value of self-inductance varies as

Similar Questions

$A$ graph of magnetic flux $(\phi)$ versus current $(I)$ is plotted for four inductors $A, B, C, D$. Which inductor has the largest value of self-inductance?

The self-inductance of a solenoid is $L$, which is made by a wire of length $l_w$. What is the length of the solenoid?

$A$ 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:

The inductance of a solenoid $0.5 \, m$ long of cross-sectional area $20 \, cm^2$ and with $500$ turns is......$mH$

$A$ 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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module