Two distinct inductors store the exact same amount of magnetic energy. If the ratio of their inductances is 1:4 , what is the ratio of the currents flowing through them?

Step-by-step solution

Let the inductances be L₁ and L₂ , and the currents be i₁ and i₂ . The magnetic energy stored in an inductor is given by U = 1 2 L i^2 . Since the energies are equal: U₁ = U₂ 1 2 L₁ i₁^2 = 1 2 L₂ i₂^2 Rearranging for the ratio of currents: ( i₁ i₂ )^2 = L₂ L₁ Given that L₁ : L₂ = 1 : 4 , we have L₂ L₁ = 4 1 . ( i₁ i₂ )^2 = 4 i₁ i₂ = 2 1 Therefore, the ratio of the currents is 2:1 . Answer: 2:1