In the circuit shown, switch's is closed at t=0. then the ratio `(U_(1))/(U_(2))` of potential energy stored in the inductors `L_(1)` and `L_(2)` in steady state is

Options

A. `(L_(1))/(L_(2))`
B. `(L_(2))/(L_(1))`
C. `((L_(1))/(L_(2)))^(2)`
D. `((L_(2))/(L_(1)))^(2)`

Answer

B

Explanation

`L_(1)(di_(1))/(dt)=L_(2)(di_(2))/(dt)` ltbr. `L_(1)underset(0)overset(i_(1))intdi_(1)=L_(2)underset(0)overset(i_(2))intdi_(2)`
`L_(1)i_(1)=L_(2)i_(2)` .(i)
`i_(1)+i_(2)=i` …(ii)
`i_(1)(1+(L_(1))/(L_(2)))=i`
`impliesi_(1)=((L_(2))/(L_(1)+L_(2)))i` and `i_(2)=((L_(1))/(L_(1)+L_(2)))i` ltbr. `therefore(U_(1))/(U_(2))=((1)/(2)L_(1)i_(1)^(2))/((1)/(2)L_(2)i_(2)^(2))=(L_(1)L_(2)^(2))/(L_(2)L_(1)^(2))=(L_(2))/(L_(1))`