1. Feb 23, 2012

### Miike012

What is the difference between
1. ΔU= Q*ΔV
2.U = 1/2*Q*ΔV

When do I use 1. and 2. ?

2. Feb 23, 2012

### PeterO

Context?
What does U, V and Q represent.

3. Feb 23, 2012

### Miike012

U: Electric poten. energy.
V: Voltage, or electric potential
Q: Charge....

But the two equations are similar but one has a factor of .5....

4. Feb 23, 2012

### Miike012

for instance what if I was asked .. what is the energy supplied by a battery in charging the capacitors... What eq. would I use?

5. Feb 23, 2012

### PeterO

Just because your height is measured in metres, doesn't mean we call it metre-age [there isn't even a word like that].

Voltage, is just "age" stuck on the end of the unit Volt.

Electric potential difference is measured in Volts - the symbol V is commonly used to represent a potential difference.

Electric potential doesn't mean a lot in so far as what current flow for example [movement of charge] that is determined by Potential Difference.

As I said - context please.

Perhaps you have written one [or both] of the equations incorrectly?

6. Feb 23, 2012

### PeterO

Where did you get the two equations? What was being discussed when they were introduced / derived?

7. Feb 23, 2012

### Miike012

The equations are correct...

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8. Feb 23, 2012

### PeterO

So why did one of the equations include q while the other included Q.

v and V are different - the first usually means velocity while the second has to do with "voltage"

9. Feb 23, 2012

### PeterO

The first formula looks like it might be the amount the energy of a charge q gains/loses when subjected to a change in V

The second looks like the Energy stored when a capacitor is charged. After the first bit, that you quoted they continue to sub for the value of a capacitor (C) , or at least I assume that is dealing with Capacitors.

10. Feb 24, 2012

### Redbelly98

Staff Emeritus
I don't see any lowercase "v" anywhere in this discussion
I agree, that is exactly what that formula is telling us. If (usually point) charge moves through a potential difference ΔV, the formula tells us the change in potential energy.
Yes, that is most certainly the energy stored in a capacitor that has a charge Q on one of it's plates, and a potential difference ΔV across the two plates.

11. Feb 24, 2012

### PeterO

OP
What is the difference between
1. ΔU= Q*ΔV
2.U = 1/2*Q*ΔV

When do I use 1. and 2. ?

I believe your final two statements - highlited in blue above - answer your own original post. Of course you have to correct 1. to read ΔU= q*ΔV like the formula you copied from your text.

EDIT: Sorry, I didn't notice post#10 was not made by OP

Last edited: Feb 24, 2012
12. Feb 24, 2012

### PeterO

The half in the second formula can be explained if you think of charging a capacitor, one point charge at a time.

The first charge you transfer is easy - the capacitor is uncharged.
The next one is just that little bit more difficult, as you have to over come the weak electric field you created when you moved the first charge across.
The third charge is just that little bit harder again.
It follows that the last charge you transfer is the hardest to achieve.

On average, the middle or halfway charge best represents the work done to get each charge across, thus the factor of 1/2 in that formula.