With your understanding of concept of Inductance, answer the questions.
An electric current can be induced in a coil by flux change produced by another coil in its vicinity or flux change produced by the same coil. The flux through a coil is proportional to the current i.e \( \phi_{B} \propto I \). If the geometry of the coil does not vary with tune then \( \displaystyle\frac{d\phi}{dt} \propto \frac{dI}{dt} \). For a closely wound coil of N turns, the same magnetic flux. is linked with all turns: i.e \( N\phi_{B} \propto I \). The constant of proportionality is called inductance which depends on geometry of coil and dielectric constant of intervining medium. Mutual inductance of a pain of coil solenoids, etc depends on their separation and relative orientation self-inductance of single coil or solenoid depends on geometry of the coil and permeability of the medium. If plays role of inertia.
The current in a coil of 1000 turns changes from 1A to 6A, producing a change of flux of \( 8.5\times10^{-4} \) weber. The self-inductance of the coil is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 170\,\mathrm{mH} \)
For a closely wound coil the same flux \( \phi \) links every turn, so the flux linkage is \( N\phi \), and the self-inductance is the flux linkage per unit current.
\( \displaystyle N\phi = L I \;\Rightarrow\; L = \frac{N\,\Delta\phi}{\Delta I} \)
\( N = 1000 \)
\( \Delta\phi = 8.5\times10^{-4}\,\mathrm{Wb} \)
\( \Delta I = 6 - 1 = 5\,\mathrm{A} \)
\( \displaystyle L = \frac{1000 \times 8.5\times10^{-4}}{5} = 0.17\,\mathrm{H} \)
\( \displaystyle L = 0.17 \times 1000\,\mathrm{mH} = 170\,\mathrm{mH} \)