Electromagnetic Induction - Self Induction
In above figure when current passing through the circuit and coil changes (increasing in our case) the magnetic flux linked with the coil also changes ,due to which an EMF will be induced in the coil(this phenomenon is called self induction) .This induced EMF and induced current will be in opposite direction(as current is increasing in our case) .
As the flux linked with the coil increases as current increases, hence flux linked with coil is directly proportional to current.
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remove proportionality sign and put constant L
Differentiate both sides wrt time
-----equation 1
By Faraday's Law , Induced EMF is given by below equation
Substitute value from equation 1 to equation 2
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