1. The problem statement, all variables and given/known data An LR circuit has a resistance R = 25 Ω, an inductance L = 5.4 mH, and a battery of EMF = 9.0 V. How much energy is stored in the inductance of this circuit when a steady current is achieved? 2. Relevant equations [itex]\epsilon[/itex]= -d[itex]\phi[/itex]_{m}/dt=-L[itex]\frac{dI}{dt}[/itex] U_{m}=[itex]\frac{1}{2}[/itex]LI^{2} L=[itex]\phi[/itex]_{m}/I 3. The attempt at a solution According to the equations, to find the energy stored in the inductance of the circuit, I need to find current, but I don't know how. For the equation of emf, by a "steady" current, I suppose this means that dI/dt is equal to zero. I don't know how that helps, but it's as far as I got trying to understand this problem. Perhaps there is an equation that is necessary to solve this problem, but nothing comes to mind. Maybe... Ohm's law? But I doubt it as the potential difference across the circuit isn't known, and I don't think emf can be substituted for potential difference V even thought they have the same units (voltage).
You are on the right track!!!!!! The steady current is simply given by I = V/R The inductance determines the RATE at which the current rises
Oh. So I was. Supposing emf can be substituted into I=V/R as V, then the standing current is equal to 9V/25 ohms= 0.36A. U_{m}= 0.5(5.4 x 10^{-3}H)(0.36A)^{2}= 3.4992 x 10^{-4}J= 0.35 x 10^{-3}J= 0.35 mJ That would be the correct answer. Thank you!