Two different coils have self-inductances `L_(1)=8mH` and `L_(2)=2mH` At a certain instance the current in thw two coils is increasing at the same constant rate and the power supplied to the coils is the same. Find the ratio of (a) induced voltage (b) current (c) energy stored i the two coils at that instant.

Explanation

(a) `e_(1)/(e_(2))=(L_(1)(di//dt))/(L_(2)(di//dt))=(L_(1))/(L_(2))=(8)/(2)=(4)/(1)`
(b) `P=e_(1)i_(1)=e_(2)i_(2)`
`(i_(1))/(i_(2))(e_(2))/(e_(2))=(1)/(4)`
(c) `(U_(1))/(U_(2))=((1)/(2)L_(1)i_(1)^(2))/((1)/(2)L_(2)i_(2)^(2))=(L_(1))/(L_(2))((e_(2))/(e_(1)))^(2)`
`=((8)/(2))((1)/(4))^(2)=(1)/(4)`