Energy stored in an inductor of an LR circuit

OmegaFury

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]LI²
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).

technician

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

OmegaFury

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^-3H)(0.36A)²= 3.4992 x 10^-4J= 0.35 x 10^-3J= 0.35 mJ

That would be the correct answer. Thank you!