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 $30 \,Wb$.
Similar Questions
Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10\ cm^2$ and length$= 20\ cm$. If one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is
$\mu_{0}=4 \pi \times 10^{-7} \;TmA ^{-1}$
Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10\ cm^2$ and length$= 20\ cm$. If one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is
$\mu_{0}=4 \pi \times 10^{-7} \;TmA ^{-1}$
- [AIEEE 2008]
A small circular loop of wire of radius $a$ is located at the centre of a much larger circular wire loop of radius $b$. The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I = I_0\, cos\, (\omega t)$ . The emf induced in the smaller inner loop is nearly
A small circular loop of wire of radius $a$ is located at the centre of a much larger circular wire loop of radius $b$. The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I = I_0\, cos\, (\omega t)$ . The emf induced in the smaller inner loop is nearly
- [JEE MAIN 2017]
What is the coefficient of mutual inductance when the magnetic flux changes by $2 \times 10^{-2}\,Wb$ and change in current is $0.01\,A$......$ henry$
What is the coefficient of mutual inductance when the magnetic flux changes by $2 \times 10^{-2}\,Wb$ and change in current is $0.01\,A$......$ henry$
A small square loop of side $'a'$ and one turn is placed inside a larger square loop of side ${b}$ and one turn $(b \gg a)$. The two loops are coplanar with thei centres coinciding. If a current $I$ is passed in the square loop of side $'b',$ then the coefficient of mutual inductance between the two loops is
A small square loop of side $'a'$ and one turn is placed inside a larger square loop of side ${b}$ and one turn $(b \gg a)$. The two loops are coplanar with thei centres coinciding. If a current $I$ is passed in the square loop of side $'b',$ then the coefficient of mutual inductance between the two loops is
- [JEE MAIN 2021]
Two coils, $X$ and $Y$, are kept in close vicinity of each other. When a varying current, $I(t)$, flows through coil $X$, the induced emf $(V(t))$ in coil $Y$, varies in the manner shown here. The variation of $I(t)$; with time, can then be represented by the graph labelled as graph
Two coils, $X$ and $Y$, are kept in close vicinity of each other. When a varying current, $I(t)$, flows through coil $X$, the induced emf $(V(t))$ in coil $Y$, varies in the manner shown here. The variation of $I(t)$; with time, can then be represented by the graph labelled as graph
- [JEE MAIN 2013]