Question 189: Electromagnetic Induction

Question

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______J.

Accepted Answer

$$L{{di} \over {dt}} = \varepsilon $$
$$ = 3t$$
$$L\int {di = 3\int {tdt} } $$
$$Li = {{3{t^2}} \over 2}$$
$$i = {{3{t^2}} \over {2L}}$$
energy, $$E = {1 \over 2}L{i^2}$$
$$ = {1 \over 2}L{\left( {{{3{t^2}} \over {2L}}} ight)^2}$$
$$ = {1 \over 2} 	imes {{9{t^4}} \over {4L}}$$
$$ = {9 \over 8} 	imes {{{{(4)}^4}} \over {4 	imes 2}} = 144$$ J

Electromagnetic Induction

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______J.

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