# Question: What is the difference between e.m.f. and Potential Difference?

1. Jan 14, 2009

### psykatic

1. The problem statement, all variables and given/known data
What is the difference between E.M.F. and Potential Difference of a circuit?

2. Relevant equations
Both have similar SI unit, that is, Volt (V)

3. The attempt at a solution
I did find out one thing, that emf is the potential difference when there is no current flowing through the circuit or when the key is open. Whereas, the circuit has certain value of potential difference when there is current flowing through the circuit.

But, while I was going through the Chapter Electromagnetic Induction, I found one thing strange. In case of an A.C circuit containing an inductance, we have,
$$e=E_o~sin({\omega.t}+{\pi/2})$$
and even, the instantaneous current is given by,
$$i=I_o sin({\omega.t)$$
Where does this current come from? How can the circuit have a current flowing through when there is certain value of e.m.f?

2. Jan 14, 2009

### LowlyPion

The key to thinking about an electromotive force is the "force". It is a force that will push current along - circuit willing.

The voltage is an expression of the potential difference between 2 points. Of course if those 2 points are on each side of an emf source they will be interchangeable in that circumstance then won't they?

3. Jan 14, 2009

### psykatic

I didnt get you, do you mean emf is a force whereas voltage isnt? Then if it is a force, how is it experienced by the circuit? and due to what factor? There is no current flowing through the circuit, yet we have equations for the instantaneous current flowing through the circuit. How is that possible?

4. Jan 14, 2009

### LowlyPion

An emf is a source of electrical energy. Like a battery or a generator actively sources electrical flow.

Voltage is a measure of electrical potential between 2 points.

In looking at Ohms Law the sum around a loop is 0. The emf is the active element and the resistors "resist" the flow from the emf about the loop, hence voltage drops to account for the electrical energy supplied by the emf.

5. Jan 15, 2009

### psykatic

So, if there is an emf source in a circuit, it automatically induces current. And these currents are alternating in nature. Is it true?

6. Jan 15, 2009

### Defennder

Not necesassarily AC current. A DC source may be considered emf as well.

7. Jan 15, 2009

### psykatic

So, their maximum value doesnt change after certain phase reversal? Thats a DC, in that case what would be the equation for instantaneous current in the circuit?

8. Jan 15, 2009

### Defennder

What do you mean by "certain phase reversal" and "instantaneous current" ?

9. Jan 15, 2009

### psykatic

As in the case of a circuit having sertain emf source connected parallel to the emf, the current induced is alternating i.e in the given equation,
$$i=I_o sin({\omega.t)$$
The value of $$I_o$$ changes with the value of the $$\omega.t$$. If we plot a graph, the value of $$I_o$$ reaches maximum when $$E_o$$ is maximum.(i.e a sine graph, with maximum values when $$\theta=\omega.t =0,\pi/2, \pi ~and~ so~ on$$

10. Jan 15, 2009

### djeitnstine

Have you ever seen a graph of AC current and a DC current together? AC obeys the laws you just stated. DC however is as the name implies is direct...so its graph is theoretically a straight line (that doesn't happen in absolutely all cases)

So Alternating Current...alternates and Direct Current doesn't

11. Jan 15, 2009

### kbaumen

Well, if you really want to have an equation for DC, then look up Ohm's law for full circuit which is $E$ = I(R + r), hence I = $E$ / (R + r) where R is the resistance of all electric components in the circuit and r is the resistance of of the electricity source. This is for DC! DC implies that current flows in one direction, so without intervention (considering an ideal circuit, where energy source contains an unlimited amount of electrical energy), current, EMF, voltage across any two points of the circuit and resistance remain constants over time. So I(t) is a straight line, parallel to x-axis. I hope that helps.

12. Jan 15, 2009

### psykatic

Okay agreed, then what is the effective value of EMF and Current all about? I mean, 've two more equations given by,
$$E_rms=\frac{E_o}{\sqrt [2]}$$

The book says, if the emf induces certain current in the circuit and this current generates certain amount Heat (H) in time t, then the same quantity of heat can be produced in the same circuit in the same time by passing a steady current of constant magnitude through it. The vale of such current is called the effective value or R.M.S. value.

Is this value a representation of DC? I'm terribly confused!

13. Jan 15, 2009

### Defennder

No the concept of RMS value is that if you can treat the AC source as though it were operating like a DC with a specified RMS value. Unlike the DC source of emf, the exact voltage supplied varies with time, so the RMS value is simply the "average" value of the AC current which could be simulated with a DC current of the same value to yield the same result. In a way, you could think of RMS value of a AC source of emf as its quasi-DC equivalent.

14. Jan 16, 2009

### psykatic

Gosh! This is getting on my nerve, is it that if a circuit has an emf source, it'll induce AC current and in case of certain applied potential difference, it'll induce DC?

15. Jan 16, 2009

### rl.bhat

We don't want any external emf source to induce AC current in a circuit. We have to rotate a coil with a resistance in a magnetic field.
We can't induce DC current in any circuit. Chemical reaction in a cell will produce DC current in the circuit.

16. Jan 16, 2009

### psykatic

Then what does this equation represent,

$$i=I_o sin({\omega.t)$$
a D.C current or an Alternating Current, it has to be AC, but then what is instantaneous current? neither DC nor AC, then what?

17. Jan 16, 2009

### rl.bhat

A small portion of any curve is almost a straight line but a curve is not a straight line. Similarly an instantaneous current is in one direction but we won't call it as DC.

18. Jan 16, 2009

### psykatic

Okay, concept clear! Thank You very much everyone!

19. Sep 4, 2011