So I finished my class in DC circuits this spring in college and learned about capacitance and inductance. To add context, I'm interesting in (stationary) energy storage, say for a tiny home. I know there are batteries but I'm curious about more affordable alternatives. Not saying I would actually use this but I just wanted to get a better idea of the potential of such things like this. Could this theoretically work?

Now the idea of using supercapacitors to store energy is explored a little bit here and there on the internet from what I've seen. And I'd have to guess that's the next best alternative to expensive batteries for storing something like solar energy, but what about inductors?

So far the questions I've seen about this imply an inductor is charge in a closed circuit which is then opened, but of course this won't work since higher resistance causes an inductor to lose energy faster. BUT: A very low resistance causes an inductor to lose energy slower! So here's the idea: What if a very high inductance inductor were charged up, then switched into a shorted loop with very little resistance, and the energy was switched into a load as needed, thus making an "inductor battery"?

 

So I finished my class in DC circuits this spring in college and learned about capacitance and inductance. To add context, I'm interesting in (stationary) energy storage, say for a tiny home. I know there are batteries but I'm curious about more affordable alternatives. Not saying I would actually use this but I just wanted to get a better idea of the potential of such things like this. Could this theoretically work?

Now the idea of using supercapacitors to store energy is explored a little bit here and there on the internet from what I've seen. And I'd have to guess that's the next best alternative to expensive batteries for storing something like solar energy, but what about inductors?

So far the questions I've seen about this imply an inductor is charge in a closed circuit which is then opened, but of course this won't work since higher resistance causes an inductor to lose energy faster. BUT: A very low resistance causes an inductor to lose energy slower! So here's the idea: What if a very high inductance inductor were charged up, then switched into a shorted loop with very little resistance, and the energy was switched into a load as needed, thus making an "inductor battery"?

Taking as an example a 4kW battery charger (because 4kW will run a small household). An inductor to supply that amount of power for 20ms is as big as a housebrick and weighs 10kg. You can extrapolate. . .

 

A typical 1.5 Tesla MRI machine's superconducting magnet can store approximately 200 million joules of energy.

...but it's superconducting

 

If the inductor is wound with a superconductor it could hold the current for a long time. If not the current will be defined but the LR time constant tau = L/R

 

If the inductor is wound with a superconductor it could hold the current for a long time. If not the current will be defined but the LR time constant tau = L/R

but could it store enough energy to run its own cryostat?

 

I must be missing something (this is quite possible having just returned from traveling and being short of sleep) but...

If an inductor which has a large magnetic field formed is shorted "it will try" to reproduce its original input current by collapsing the magnetic field and inducing current into the short... which would be... very warm, no?

What am I missing?

 

If it is supercooled, it might not get warm, depending upon the capabilities of the coolin system.

I seem to remember a time when the Large Hadron Collider had an overheating problem which took over a year before they went back online.

 

If it is supercooled, it might not get warm, depending upon the capabilities of the coolin system.

Yes, but practically speaking since the application is energy storage for efficiency, supercooling isn't an option—is it? In the case of some very special application, supercooling an inductor to maintain it's field into a short might have some use, but...

 

Agreed, not an efficient way to store energy.

I we think about we use inductors to store energy, often for only microseconds.

 

Agreed, not an efficient way to store energy.

I we think about we use inductors to store energy, often for only microseconds.

Yes, just like caps, even the use in simple pi filters on AC driven power supplies uses the inductor to store energy and give it back when there is a voltage drop (many times per second).

 

I must be missing something (this is quite possible having just returned from traveling and being short of sleep) but...

If an inductor which has a large magnetic field formed is shorted "it will try" to reproduce its original input current by collapsing the magnetic field and inducing current into the short... which would be... very warm, no?

What am I missing?

The current remains the same (at least for Δt seconds) the heat dissipation is still I^2.R so it also remains the same. The resistance of the short is zero, so it dissipates zero.
A Schottky diode across a relay coil is almost a short (clamps the voltage to 0.3V or so) when the relay coil is de-energised.

 

The current remains the same (at least for Δt seconds) the heat dissipation is still I^2.R so it also remains the same. The resistance of the short is zero, so it dissipates zero.
A Schottky diode across a relay coil is almost a short (clamps the voltage to 0.3V or so) when the relay coil is de-energised.

In practice, the resistance of the short isn’t 0, though—that’s the trouble. And, to approach 0Ω usefully, the size of the conductors involved… well, let’s say they would be unusually large.

 

The problem is that very high inductance and very low resistance are mutually exclusive.

Let’s for example posit a 10H inductor and 0.1Ω resistance. It would self discharge in a few mnutes.

L / R = 10 / 0.1 = 100 second time contant.

 

I saw one article about a current probe with a very long time constant. The amplifier provided a negative resistance to cancel the resistance of the inductor, making L/R huge. I built the circuit and was amazed to see the voltage on the amplifier track the field as I slowly moved a permanent a magnet across the current transformer. It seemed then low frequency cutoff was a fraction of a Hz.

 

I must be missing something (this is quite possible having just returned from traveling and being short of sleep) but...

If an inductor which has a large magnetic field formed is shorted "it will try" to reproduce its original input current by collapsing the magnetic field and inducing current into the short... which would be... very warm, no?

What am I missing?

Hi there,

If the current is *already* there it does not have to collapse the field. It's only when the current has to change that the field has to change. If the current is a constant 1 amp then it can stay at 1 amp without changing the field.

That might be the key point, but of course this is in pure theory. In real life most of the applications we run into are regular room temperature stuff, so there's going to be some resistance in the inductor wire coil so that 1 amp is accompanied by a voltage and as we all know P=E*I and so we get power dissipation as heat, and that eventually eats up all the energy.

The superconducting application is of course different because there is no heat. That's not easy to do though and not very typical of the stuff we run into every day.

We could look at a circuit and show that when R goes to zero the current stays constant over time. That would be in circuit theory though not pure physics, but it may help to see what is happening anyway.

In a physical situation we would have a flywheel with a bearing that has zero resistance. The wheel will turn forever. Even the slightest drag from an imperfect bearing though will start to eat up energy and the wheel will eventually come to a stop. The time it takes is dependent on the friction and the mass.
That's a rotational system, but we have a similar situation in the translational system too. In both cases something goes on forever unless there is something to make it change such as friction or some other force. That's how inertia works.

Another view is that the inductor-with-current is the dual of the capacitor-with-voltage.
The open circuited capacitor holds a voltage forever unless there is some parallel leakage resistance.
The shorted inductor holds a current forever unless there is some series resistance (or some other resistance).