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# In an induction coil, the coefficient of mutual induction is $4H$. If a current of $5A$ in the primary coil in cut off in $\dfrac{1}{{1500}}s$, the emf at the terminals of secondary coil will be$\left( A \right)10kV$$\left( B \right)15kV$$\left( C \right)30kV$$\left( D \right)60kV$

Last updated date: 16th Jun 2024
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Hint:Mutually induced emf is defined as the emf induced in a coil due to the change of flux produced due to another neighboring coil linking to it. Apply the formula of emf of mutual induction and find the emf at the terminals of secondary coil using the above data.

Formula used:
$e = M\dfrac{{dI}}{{dt}}$
Where $e$ is the emf of mutual induction, $I$ is the current and $t$ is the time and $M$ is mutual induction.

Complete step by step solution:
The property of the coil due to which it opposes the change of current in the other coil is called mutual inductance between two coils. When the current in the other coil or neighboring coil changes, a changing flux emf is induced in the coil. It is called mutual induced emf. The mutual inductance depends on cross sectional area, closeness of two coils and number of turns in the secondary coil.
Permeability of the medium surrounding the coils is directly proportional to mutual inductance. The magnetic field in one of the coils tends to link with each other when the two coils are brought close with each other. This property of coil changes the current and voltage in the secondary coil.
$e = M\dfrac{{dI}}{{dt}}$
Where $e$ is the emf of mutual induction, $I$ is the current and $t$ is the time.
In the given data is $M = 4H$, $I = 5$ and $t = \dfrac{1}{{1500}}s$
$e = \dfrac{{4 \times 5}}{{\dfrac{1}{{1500}}}}$
$e = 30000V = 30kV$

Hence option (C) is the correct option

Note: A galvanometer connected to the coil measures the induced emf. The flux linking with other coils changes when the current flowing through the primary coil is changed to the value of variable resistor $R$.