One has a 120v battery. One attaches a 200M wire across the terminals. Is the voltage the same between all...?
I am thinking of it like a large hill where the highest gravitational potential energy is at the top of the hill and the bottom has zero potential energy. I don't think the difference in potential energy is the same between all two points on the hill.
So I think that the if you take the potential difference (voltage) across two points an inch apart on the wire the voltage won't be very large at all. But another part of me thinks the voltage (potential difference) is the same between any two points on the wire attached to the 120V battery. Please help me to understand. Thanks a great deal.
Answer:
Let us suppose that the wire in question is uniform in composition and cross section, and the wire is 120 inches long, if we measure between any two points 1 inch apart, we will find the same reading, which will be 1 volt, not 120volts. If we sum the voltage of all 120, non-overlapping, one inch sections, of the wire, we get 120v which is the total being applied to the wire.
If you have taken simple electronics you will know about NODES if they are present then the current is the same going into the node and out of the node.
With a theoretical perfect conductor the potential would be equal everywhere, but yes Virginia there is such a thing as resistance. The long wire is actually a long resistor and so voltage readings from A or B to the middle would be lower than the potential between A and B. Current is something else. Suppose your 200 mile wire has 500 ohms per mile. Then your 120 volts will produce a current flow through the wire of 1.2 milliamperes, not much. Of course in that first mini micro second when it is first turned on, I guess the electrons flow in some fashion (supposedly from negative to positive) but that's a question for a real physicist.
If we can assume the wire has a uniform cross sectional area along the entire length then any one cm of the wire will have the same potential across it as any other one cm. Two cm with have twice as much potential as one cm. Two points 1m apart will have a difference in voltage 100 times as grate as any two points 1 cm apart.
In theory, yes there is a potential difference due to the resistance between the two points even though it looks like negligible but still there is. But in actual, due to the resistance of the wire is so small then looks like you are short circuiting the battery. Depends upon the capacity of the battery either it will burned the wire or the voltage will drop to zero.
You should check out Ohms Law on this.
V=I*R Voltage = current * resistance
The long wire is a resistor. The longer the wire, or the more distance between measured points, the more resistance.
Since the current thru the wire will be the same the potential difference between any set of equally spaced points will also be the same.
It's important to remember that voltage, or potential difference, measures the difference between two points. If you were to perform this as an experiment your volt meter would give a small reading when the points are close together and the voltage would increase as the points got farther apart. This seems counter intuitive but it does follows Ohms law.
A better experiment would be to measure a point on the wire relative to a ground. This would give a reading of battery voltage at the battery terminal and the voltage would drop as you moved along the wire.
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