Explain Inductance. Give its unit and dimensions. - Vidyadip

Question

Explain Inductance. Give its unit and dimensions.

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Answer

→Induced current is formed when magnetic flux linked with any coil is changed,
(i) by changing electric current passing through coil itself
OR
(ii) by changing electric current passing through another coil placed nearby.
→In above both cases, magnetic flux $\phi_{ B }$ linked with coil is directly proportional to electric current I .
$\therefore \phi_{ B } \propto I$
→If dimensions of coil do not change with time, then
$\frac{d \phi_{ B }}{d t} \propto \frac{d I }{d t}$
→If coil has N closely wound turns, then total magnetic flux linked will be $N \phi_{ B }$ which is
also indirectly proportional to electric current passing through coil.
$N \phi_{ B } \alpha I$
The constant of proportionality in equation (1) & (3) is called Inductance.
→Inductance is a scalar quantity. It depends on dimensions (geometry and shape) of coil, intrinsic properties of material of coil and medium on which coil is wound.
→SI unit of inductance : Henry (H)
→Dimensions : $M ^1 L^2 T^{-2} A^{-2}$
→Other Units :
Wb. $A ^{-1}$, T. $m^2 A^{-1}, N . m . A ^{-2}, \Omega sec$,
V.sec. $A ^{-1}$, V.C. $A ^{-2}, J.A^{-2}$

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