A solenoid has an inductance of 10 henry and a resistance of 2 ohm. It is connected to a 10 volt battery. How long will it take for the magnetic energy to reach `1//4` of its maximum value?

Answer

c

Explanation

The current grows in L-R circuit till steady state is reached.
At stedy, state, energy stored in indctor is maximum.
At steady state, cuirrent =`I_(0)`
At some instant of time current=1
`:.` Maximum energy `=(1)/(2)LI_(0)^(2)`
Energy stored when current is `I=(1)/(2)LI^(2)`
`:.(U_("max"))/(U)=(2LI_(0)^(2))/(2LI^(2))`
`(U_("max"))/((U_("max")/(4)))=((I_(0))/(I))^(2)`
`or ((I_(0))/(I))^(2)=4`
`or I=(I_(0))/(2)" ".....(i)`

For growth of current in L-R circuit,
`I=I_(0)[1-e^((R)/(L)t)]or (I_(0))/(2)=I_(0)[1-e^((2)/(10)t)]`
`or (1)/(2)=1-e^(-t//5)`
`e^(-t//5)=(1)/(2)`
or `t=5 ln 2`
`or t=5xx0.963`
or `t=3.465s`