આકૃતિમાં દર્શાવ્યા મુજબ એક ગૂંચળામાં વિદ્યુતપ્રવાહ $i$ એ સમય સાથે બદલાય છે. ગૂંચળામાં સમય સાથે બદલાતા પ્રેરિત $e.m.f.$ માટે કયો આલેખ યોગ્ય છે.

Question

AIPMT 2011, Diffcult

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Solution

a
Induced $emf$, $e=-L \frac{a_{l}}{d t}$

For $0 \leq t \leq \frac{T}{4}$

$i-t$ graph is a straight line with positive constant slope.

$\therefore \quad \frac{d i}{d t}=$ constant

$\Rightarrow e=-v e \text { and constant } $

$ \text { For } 0 \leq t \leq \frac{T}{4}$

For $\frac{T}{4} \leq t \leq \frac{T}{2}$

$i$ is constant $\therefore \frac{d i}{d t}=0$

$\Rightarrow \quad e=0$

For $\frac{T}{4} \leq t \leq \frac{T}{2}$

For $\frac{T}{2} \leq t \leq \frac{3 T}{4}$

$i-t$ graph is a straight line with negative constant slope.

$\therefore \frac{d i}{d t}=$ constant

$\Rightarrow e=+$ $ve$ and constant

For $\frac{T}{2} \leq t \leq \frac{3 T}{4}$

For $\frac{3 T}{4} \leq t \leq T$

$i$ is zero $\therefore \frac{d i}{d t}=0$

$\Rightarrow e=0 \quad \text { For } \frac{3 T}{4} \leq t \leq T$

From this analysis, the variation of induced $emf$ with time as shown in the figure below.

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