Question: Q. 6. (i) Define mutual inductance.
(ii) A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to $20 \mathrm{~A}$ in $0.5 \mathrm{~s}$, what is the change of flux linkage with the other coil ? $R$ A [Delhi I, II, III 2016]
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Solution:
Ans. (i) Magnetic flux, linked with the secondary coil due to the unit current flowing in the primary coil,
[Alternatively,
$$ \begin{equation*} \phi_{2}=M I_{1} \tag{1} \end{equation*} $$
Induced emf associated with the secondary coil, for a unit rate of change of current in the primary coil.
$$ \begin{equation*} \left.e_{2}=-M \frac{d I_{1}}{d t}\right] \tag{1} \end{equation*} $$
[Also accept the definition of Mutual Induction, as per the Hindi translation of the questions]
[i.e., the phenomenon of production of induced emf in one coil due to change in current in neighbouring coil]
(ii) Change of flux linkage
$$ \begin{aligned} d \phi & =M d I \ & =1.5 \times(20-0) \mathrm{W} \ & =30 \text { weber } \end{aligned} $$
Detailed Answer :
[CBSE Marking Scheme, 2016]
(i) Try yourself, Similar to Q. 1 (a), Short Answer Type Questions-II
(ii) Given :
Mutual inductance of a pair of coils, $\mu=1.5 \mathrm{H}$ Initial current,
Final current
Change in current willb
$$ \begin{aligned} \Delta 1 & =l_{2}-l_{1} \ 20-0 & =20 A \end{aligned} $$
and we know,
where,
$$ \Delta \phi=M \Delta I $$
$\Delta \phi$ is change in magnetic flux
$$ \begin{aligned} \Delta \phi & =1.5 \times 20 \ & =30 \mathrm{~Wb} \end{aligned} $$
Hence, change in the flux linkage will be $30 \mathrm{~Wb}$.
[1] Q. 7. Define the term self-inductance of a solenoid. Obtain the expression for the magnetic energy stored in an inductor of self-inductance $L$ to build up a current $I$ through it. $R$ [O.D. I, II, III 2014]
Ans. Try yourself, Similar to Q. 2, Short Answer Type Questions-I
