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Define salf-inductance of a coil. Obain the expression for the energy stored in an inductor L connected across a source of emf. |
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Answer» Solution :Selfinductanceis defined as the magenetic flux linked with the coil when UNIT current flows through it  Let current I flow through a,coil at any instant, then the magnetic flux `phi` , linked with the coil is found to be proportional to the strength of the current(I). `phi alpha Ior , phi = LI` Where L = self inductence , a constant of proportionality. Let, an indicator of inductance L. be connected across a battery when current I flowes throuth through the inductor , an emf `in` is induced in it. This induced emf is given by ` in = - L (dI)/(dt)`...(i) The-ve sign have implies that `'in`' opposes the passage of current I in the conductor. To drive the current through the inductor against the induced emf`'in`', the external valtage is applied . External valtage = - `in` From (i) ` in = L (dl)/(dt)` Let an infinitesimal change dq be driven through the inductor . So , the work DONE by the external suppley is given by, `domega = omega dq or domega= L (dl)/(dt) dq ` `domega = LdI(dq)/(dt) , rArr d omega = LIdItherefore(dq)/(dt) = 1` Total wark done to maintain the MAXIMUM value of current `(I_(0))`through the inductor is `intdomega = underset(0)overset (I)overset(0)intLIdI rArromega = L ((I^(2))/(2))_(0)^(I_(0))` `omega = L (I_(0)^(2))/(2) rArromega = (1)/(2)LI _(0)^(2)` This work done is STORED as the magnetic field energy u in the inductor and n`= 1//2L I^(2)` . |
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