# Energy stored in an inductor

1. Nov 13, 2005

I need a little help here.
The question says to consider an inductor with L=16H and an internal resistance of 0.10 ohms. We wish to use this inductor to store 0.10 MJ of energy. What is the rate at which energy is lost to Joule heating in this system? It is not practical to store large amounts of energy in large inductors unless the wire is superconducting.

my work: I know the energy stored in an inductor is 1/2*LI^2. So how would I find the current given the information? And is the rate found by multiplying current by the emf?

Am I far off?

2. Nov 14, 2005

### Andrew Mason

The I in this expression represents the final current in the inductor. The energy builds as the current increases and is stored in the magnetic field of the inductor. But some is lost to heating the conductor. The power lost by this current to resistance of the wire is the quantity you are trying to find. Use the expression for power loss (P) in terms of I and R. and integrate that as I goes from 0 to $\sqrt{2E/L}$:

$$E_{loss} = \int_0^{\sqrt{2E/L}} Pdt$$

AM

3. Nov 14, 2005