A pair of adjacent coils has a mutual inductance of $1.5\; H$. If the current in one coil changes from $0$ to $20\; A$ in $0.5\; s ,$ what is the change of flux (in $Wb$) linkage with the other coil?
A pair of adjacent coils has a mutual inductance of $1.5\; H$. If the current in one coil changes from $0$ to $20\; A$ in $0.5\; s ,$ what is the change of flux (in $Wb$) linkage with the other coil?
Mutual inductance of a pair of coils, $\mu=1.5\, H$
Initial current, $I_{1}=0 \, A$
Final current $I_{2}=20\, A$
Change in current, $d I=I_{2}-I_{1}=20-0=20.4$
Time taken for the change, $t=0.5\, s$
Induced $emf$, $e=\frac{d \phi}{d t}. . .(i)$
Where $d \phi$ is the change in the flux linkage with the coil. $Emf$ is related with mutual inductance as:
$e=\mu \frac{d I}{d t}...(i)$
Equating equations $(i)$ and $(ii),$ we get
$\frac{d \phi}{d t}=\mu \frac{d I}{d t}$ $d \phi=1.5 \times(20)$
$=30\, Wb$
Hence, the change in the flux linkage is $30 \,Wb$.
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