# Electromotive Force

1. Nov 9, 2014

### tonyjk

Hello,
In an electrical circuit, let's say we have an AC voltage source In addition, we have an Inductor that stores electrical energy when the current is rising than give back this energy to the voltage source when the current is falling. My question is,at the stage when the energy is given back to the voltage source, how the current inside the voltage source will be against the EMF? is it the Conservative electric field of the voltage source that is driving the current inside it at this stage?

Thank you

2. Nov 9, 2014

### Philip Wood

The line integral of any conservative field around the whole circuit is zero. What drives the current is the algebraic sum of the emf induced in the coil due to the falling flux and the emf of the supply, at any instant.

The first sentence above, I think, is indisputable. The question is: is it relevant? In particular does the second sentence follow from it. I rather think it does, inasmuch as the correct equation is $|emf_{supply}| - |emf_{coil}| = |IR|$. There is no potential difference term. I regard all terms, including $IR$, as work terms. I suspect this is controversial.

Last edited: Nov 9, 2014
3. Nov 10, 2014

### Philip Wood

Correction: please remove modulus signs ( | ).

4. Nov 10, 2014

### tonyjk

Thanks Philip, but let's say the voltage source is constant and positive but the current is negative, how the current is circulating inside the source against the EMF?

5. Nov 10, 2014

### Philip Wood

I'm confused. Are we no longer dealing with an ac voltage source, as in your original post?

What is the circuit? Is it simply a coil connected across a voltage source? If so, is it a constant voltage source or alternating?

If it's a constant voltage source, the current will never be negative (if you mean in the opposite direction from that of the supply emf). The current will rise, but more and more slowly.

I'm not trying to be awkward; I simply don't understand the set-up.

6. Nov 10, 2014

### tonyjk

Yes Sorry Philips, I mean that for AC Supply, sometime the source has positive voltage and the current is negative

7. Nov 10, 2014

### Philip Wood

Try this...

#### Attached Files:

• ###### emfs.jpg
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8. Nov 10, 2014

### tonyjk

Yes Philip the EMF of the coil is driving the current when it is negative, so we can say because of the continuity of the current in a series circuit, the current will be the same inside the Voltage source right? but there is no "physical" description of why this is happening inside the voltage source

9. Nov 10, 2014

### Philip Wood

I think you're asking some quite deep questions. In the resistance-less set-up we're considering, the two emfs (source and coil) are always equal and opposite. The current doesn't need 'driving' round, because theres's no resistance. The current, as you say, will be the same all the way round. I suppose that it flows round the circuit rather like water in a heating system, because if electrons started to pile up in one place the region would become negatively charged and the pile-up could not continue, so I think conservative forces do play a part in the flow to this extent. These are deep waters.

Last edited: Nov 10, 2014
10. Nov 10, 2014

### tonyjk

Okay great Thanks a lot Philip