Two coils have self inductance L₁ and L₂ . The current through them is increasing at constant rate. If the power dissipated in both the coils is same, then the ratio of energy stored in the coil having inductance L₁ to that in L₂ is

Step-by-step solution

Power supplied to an inductor is given by P = | | i = L di dt i Given that the current is increasing at a constant rate, di₁ dt = di₂ dt = k Since the power dissipated in both coils is the same, P₁ = P₂ L₁ k i₁ = L₂ k i₂ L₁ i₁ = L₂ i₂ i₁ i₂ = L₂ L₁ The energy stored in an inductor is U = 1 2 L i^2 The ratio of energy stored is U₁ U₂ = 1 2 L₁ i₁^2 1 2 L₂ i₂^2 = L₁ L₂ ( i₁ i₂ )^2 Substituting the ratio of currents, we get: U₁ U₂ = L₁ L₂ ( L₂ L₁ )^2 = L₂ L₁ Answer: L₂ L₁