Question

║The Self-induced emf of a coil is 25 volts, When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is The Self-induced emf of a coil is 25 volts, When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is ?


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Answer 1

Question :

• The Self-induced EMF of a coil is 25 volts, When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is

Solution :

As per the given data ,

• EMF = 25 V
• Initial current = 10  A
• Final current = 25 A
• Time = 1 s

EMF is induced in the coil due to the change in the flow of current .

EMF induced is given by ,

$\leadsto e = L\dfrac{ \Delta I }{ t }$

On rearranging ,

$\leadsto L = \dfrac{e \times t }{\Delta I }$

Now let's substitute the given values in the above equation ,

$\leadsto L = \dfrac{25 \times 1 }{25 - 10 }$

$\leadsto L = \dfrac{5 }{3 }H$

Energy stored in the inductor is given by the formula ,

$\leadsto E = \dfrac{1}{2}LI^2$

$\leadsto \Delta E = \dfrac{1}{2}L(I_f^2- I_i^2)$

$\leadsto \Delta E = \dfrac{1}{2}\times \dfrac{5}{3}(625- 100)$

$\leadsto \Delta E = \dfrac{1}{2}\times \dfrac{5}{3} \times 525$

$\leadsto \boxed{ \Delta E = 437.5 J }$

The change in energy of the inductance is 437.5 J .