Energy stored in an inductor of an LR circuit

[OmegaFury]

Homework Statement

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?

Homework Equations

\epsilon= -d\phi_m/dt=-L\frac{dI}{dt}
U_m=\frac{1}{2}LI²
L=\phi_m/I

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]

You are on the right track!

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!