In the given circuit below inductance values of L₁ , L₂ and L₃ are same. The magnetic energy stored in the entire circuit is (U_t) and that stored in the L₂ inductor is (U_l) . U_t / U_l is __________. (Ignore the mutual inductance if any)

Step-by-step solution

Let the inductance of each inductor be L , so L₁ = L₂ = L₃ = L . Let the total current flowing through the circuit be I . This current flows entirely through L₁ . Since L₂ and L₃ are connected in parallel and have equal inductances, the current I divides equally between them. Therefore, the current through L₂ is I 2 and the current through L₃ is I 2 . The magnetic energy stored in an inductor is given by U = 1 2 L i^2 . The energy stored in the inductor L₂ is: U_l = 1 2 L ( I 2 )^2 = 1 8 L I^2 The equivalent induct