Question
Write two definitions of mutual inductance. State what it depends on and state its unit and dimensional formula.
✓
Answer
$\begin{array}{c}\text { (I) } \varepsilon_2=- M _{21} \frac{d I _1}{d t} \\
\text { If } \frac{d I _1}{d t}=1 \frac{ A }{ S } \\
\text { so, } \varepsilon_2=- M _{21}\end{array}$
→"In a system consisting of two windings; if the rate of change of current in one winding is unity, the emf induced in the other winding is called mutual inductance of the two winding system."
(II) $\phi_2= M _{21} I _1$
If $I _1=1 A$ thus $\phi_2= M _{21}$
→"In a system consisting of two windings; when the current through one winding is unity the magnetic flux associated with the other winding is called the mutual inductance of the system of two winding.
• Mutual inductance depends on the following factors :
(1) shape of coil
(2) their dimensions
(3) Number of turns
(4) Magnetic properties of the medium between the coil
(5) Their relative bowing
(6) Their relative distance.
→Unit : $H , \frac{ Wb }{ A }, \frac{ V s}{A}$
→Dimensional Formula : $M ^1 L^2 T^{-2} A^{-2}$
\text { If } \frac{d I _1}{d t}=1 \frac{ A }{ S } \\
\text { so, } \varepsilon_2=- M _{21}\end{array}$
→"In a system consisting of two windings; if the rate of change of current in one winding is unity, the emf induced in the other winding is called mutual inductance of the two winding system."
(II) $\phi_2= M _{21} I _1$
If $I _1=1 A$ thus $\phi_2= M _{21}$
→"In a system consisting of two windings; when the current through one winding is unity the magnetic flux associated with the other winding is called the mutual inductance of the system of two winding.
• Mutual inductance depends on the following factors :
(1) shape of coil
(2) their dimensions
(3) Number of turns
(4) Magnetic properties of the medium between the coil
(5) Their relative bowing
(6) Their relative distance.
→Unit : $H , \frac{ Wb }{ A }, \frac{ V s}{A}$
→Dimensional Formula : $M ^1 L^2 T^{-2} A^{-2}$
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