A coil of inductance L is divided into 6 equa | vedclass

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

Question

(B) The inductance of a solenoid is given by $L = \frac{\mu_0 N^2 A}{l}$,which implies $L \propto \frac{N^2}{l}$.When a coil is divided into $n = 6$ e

Vedclass · Accepted Answer

$\frac{L}{36}$

Vedclass · Answer

(B) The inductance of a solenoid is given by $L = \frac{\mu_0 N^2 A}{l}$,which implies $L \propto \frac{N^2}{l}$.When a coil is divided into $n = 6$ equal parts,the number of turns in each part becomes $N' = \frac{N}{6}$ and the length of each part becomes $l' = \frac{l}{6}$.The inductance of each part $L'$ is given by $L' = L \left( \frac{N'}{N} \right)^2 \left( \frac{l}{l'} \right) = L \left( \frac{1}{6} \right)^2 \left( \frac{l}{l/6} \right) = L \left( \frac{1}{36} \right) (6) = \frac{L}{6}$.When these $6$ parts are connected in parallel,the equivalent inductance $L_e$ is given by $\frac{1}{L_e} = \sum \frac{1}{L'} = \frac{1}{L'} + \frac{1}{L'} + \dots + \frac{1}{L'} = \frac{6}{L'}$.Substituting $L' = \frac{L}{6}$,we get $\frac{1}{L_e} = \frac{6}{L/6} = \frac{36}{L}$.Therefore,$L_e = \frac{L}{36}$.

$A$ coil of inductance $L$ is divided into $6$ equal parts. All these parts are connected in parallel. The resultant inductance of this combination is

Similar Questions

The equivalent inductance of two inductances is $2.4 \, H$ when connected in parallel and $10 \, H$ when connected in series. The difference between the two inductances is .......... $H$.

Two identical induction coils,each of inductance $L$,are joined in series and placed very close to each other such that the winding direction of one is exactly opposite to that of the other. What is the net inductance?

The inductance between $A$ and $D$ is

Three inductances are connected as shown in the figure. The equivalent inductance between $A$ and $B$ is (in $H$)

Two pure inductors each of self inductance $L$ are connected in parallel but are well separated from each other. The total inductance is

Vedclass Test Series

Exam Paper Generator

Online Exam Module