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1.Units, Dimensions and Measurement
medium
The dimension of mutual inductance is ............
A$\left[ ML ^{2} T ^{-2} A ^{-1}\right]$
B$\left[ ML ^{2} T ^{-3} A ^{-1}\right]$
C$\left[ ML ^{2} T ^{-2} A ^{-2}\right]$
D$\left[ ML ^{2} T ^{-3} A ^{-2}\right]$
(JEE MAIN-2022)
Solution
$e _{2}$ : induced emf in secondary coil
$i _{1}:$ Current in primary coil
$M$ : Mutual inductance
$e _{2}=- M \frac{ di _{1}}{ dt }$
$M =-\frac{ e _{2}}{\frac{ di }{ dt }}$
${[ M ]=\frac{\left[ e _{2}\right]}{\left[\frac{ di _{1}}{ dt }\right]}=\frac{\left[\frac{ W }{ q }\right]}{\left[\frac{ di _{1} }{ dt }\right]}=\frac{\left[ ML ^{2} T ^{-2}\right]}{\left[ \frac {AT}{AT^{-1}}\right]}}$
$=\left[ ML ^{2} T ^{-2} A ^{-2}\right]$
$i _{1}:$ Current in primary coil
$M$ : Mutual inductance
$e _{2}=- M \frac{ di _{1}}{ dt }$
$M =-\frac{ e _{2}}{\frac{ di }{ dt }}$
${[ M ]=\frac{\left[ e _{2}\right]}{\left[\frac{ di _{1}}{ dt }\right]}=\frac{\left[\frac{ W }{ q }\right]}{\left[\frac{ di _{1} }{ dt }\right]}=\frac{\left[ ML ^{2} T ^{-2}\right]}{\left[ \frac {AT}{AT^{-1}}\right]}}$
$=\left[ ML ^{2} T ^{-2} A ^{-2}\right]$
Standard 11
Physics
