Two different coils have self-inductance 3L and L . The current in both the coils is increased at the same constant rate. At certain instant of time, the power given to the two coils is same. At that time there was current and voltage induced in the two coils. At the same instant, the ratio of energy stored in the first coil to that in the second coil is

Step-by-step solution

Let the self-inductances of the two coils be L₁ = 3L and L₂ = L . The rate of change of current is the same for both coils, so di₁ dt = di₂ dt . The induced voltage in a coil is given by V = L di dt . For the two coils, the induced voltages are: V₁ = 3L di₁ dt V₂ = L di₂ dt The power given to the coils is P = Vi . Since the power is the same at the given instant: P₁ = P₂ V₁ i₁ = V₂ i₂ 3L di₁ dt i₁ = L di₂ dt i₂ 3 i₁ = i₂ The energy stored in an inductor is U = 1 2 L i^2 . The ratio of the energy stored in the first