Question 98: Electromagnetic Induction

Question

The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is :

Accepted Answer

Magnetic energy, U = $${1 \over 2}$$LI$$_0^2$$
Given : U = 25% of U
0
.
$$ \Rightarrow $$ $${1 \over 2}L{I^2} = {1 \over 4} 	imes {1 \over 2}LI_0^2$$
$$ \Rightarrow {I^2} = {{I_0^2} \over 4} \Rightarrow I = {{{I_0}} \over 2}$$
$$ 	herefore $$ $$I = {I_0}(1 - {e^{ - t/	au }})$$
$$ \Rightarrow {{{I_0}} \over 2} = {I_0}(1 - {e^{ - t/	au }})$$
$$ \Rightarrow {1 \over 2} = {e^{ - t/	au }}$$
$$ \Rightarrow {e^{t/	au }} = 2$$
$$ \Rightarrow t = 	au \ln 2$$
$$ \Rightarrow t = {L \over R}\ln 2$$

Answer

infinite

Answer

$${L \over R}$$ ln10

Answer

$${L \over R}$$ ln2

Answer

$${L \over R}$$ ln5

Electromagnetic Induction

The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is :

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