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Electric Currents

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Electric Currents

Topic 5.1 Electric potential difference, current and resistance

- If you want to move a charge closer to a charged sphere you have to push against the repulsive force
- You do work and the charge gains electric potential energy.
- If you let go of the charge it will move away from the sphere, losing electric potential energy, but gaining kinetic energy.

- When you move a charge in an electric field its potential energy changes.
- This is like moving a mass in a gravitational field.

- The electric potential V at any point in an electric field is the potential energy that each coulomb of positive charge would have if placed at that point in the field.
- The unit for electric potential is the joule per coulomb (J C‑1), or the volt (V).
- Like gravitational potential it is a scalar quantity.

- In the next figure, a charge +q moves between points A and B through a distance x in a uniform electric field.
- The positive plate has a high potential and the negative plate a low potential.
- Positive charges of their own accord, move from a place of high electric potential to a place of low electric potential.
- Electrons move the other way, from low potential to high potential.

- In moving from point A to point B in the diagram, the positive charge +q is moving from a low electric potential to a high electric potential.
- The electric potential is therefore different at both points.

- In order to move a charge from point A to point B, a force must be applied to the charge equal to qE
- (F = qE).
- Since the force is applied through a distance x, then work has to be done to move the charge, and there is an electric potential difference between the two points.
- Remember that the work done is equivalent to the energy gained or lost in moving the charge through the electric field.

- Potential difference
- We often need to know the difference in potential between two points in an electric field
- The potential difference or p.d. is the energy transferred when one coulomb of charge passes from one point to the other point.

- The diagram shows some values of the electric potential at points in the electric field of a positively‑charged sphere
- What is the p.d. between points A and B in the diagram?

- When one coulomb moves from A to B it gains 15 J of energy.
- If 2 C move from A to B then 30 J of energy are transferred. In fact:

- Energy transferred,
- This could be equal to the amount of electric potential energy gained or to the amount of kinetic energy gained
- W =charge, q x p.d.., V
(joules) (coulombs)(volts)

- One electron volt (1 eV) is defined as the energy acquired by an electron as a result of moving through a potential difference of one volt.
- Since W = q x V
- And the charge on an electron or proton is 1.6 x 10-19C
- Then W = 1.6 x 10-19C x 1V
- W = 1.6 x 10-19 J
- Therefore 1 eV = 1.6 x 10-19 J

- A copper wire consists of millions of copper atoms.
- Most of the electrons are held tightly to their atoms, but each copper atom has one or two electrons which are loosely held.
- Since the electrons are negatively charged, an atom that loses an electron is left with a positive charge and is called an ion.

- The diagram shows that the copper wire is made up of a lattice of positive ions, surrounded by free' electrons:
- The ions can only vibrate about their fixed positions, but the electrons are free to move randomly from one ion to another through the lattice.
- All metals have a structure like this.

- The free electrons are repelled by the negative terminal and attracted to the positive one.
- They still have a random movement, but in addition they all now move slowly in the same direction through the wire with a steady drift velocity.
- We now have a flow of charge ‑ we have electric current.

- Current is measured in amperes (A) using an ammeter.
- The ampere is a fundamental unit.
- The ammeter is placed in the circuit so that the electrons pass through it.
- Therefore it is placed in series.
- The more electrons that pass through the ammeter in one second, the higher the current reading in amps.

- 1 amp is a flow of about 6 x 1018 electrons in each second!
- The electron is too small to be used as the basic unit of charge, so instead we use a much bigger unit called the coulomb (C).
- The charge on 1 electron is
only 1.6 x 10‑19 C.

- In fact:

Or I = Δq/ Δt

Current is the rate of flow of charge

- Which way do the electrons move?
- At first, scientists thought that a current was made up of positive charges moving from positive to negative.
- We now know that electrons really flow the opposite way, but unfortunately the convention has stuck.
- Diagrams usually show the direction of `conventional current' going from positive to negative, but you must remember that the electrons are really flowing the opposite way.

- A tungsten filament lamp has a high resistance, but connecting wires have a low resistance.
- What does this mean?
- The greater the resistance of a component, the more difficult it is for charge to flow through it.

- The electrons make many collisions with the tungsten ions as they move through the filament.
- But the electrons move more easily through the copper connecting wires because they make fewer collisions with the copper ions.

- Resistance is measured in ohms (Ω) and is defined in the following way:
- The resistance of a conductor is the ratio of the p.d.applied across it, to the current passing through it.

- In fact:

- Resistors are components that are made to have a certain resistance.
- They can be made of a length of nichrome wire.

- The current through a metal wire is directly proportional to the p.d. across it (providing the temperature remains constant).
- This is Ohm's law.
- Materials that obey Ohm's law are called ohmic conductors.

- What do the current‑voltage graphs tell us?

- When X is a metal resistance wire the graph is a straight line passing through the origin: (if the temperature is constant)
- This shows that: Iis directly proportional to V.
- If you double the voltage, the current is doubled and so the value of V/I is always the same.
- Since resistance R =V/I, the wire has a constant resistance.
- The gradient is the resistance on a V against I graph, and 1/resistance in a I against V graph.

- When X is a filament lamp, the graph is a curve, as shown:

- Doubling the voltage produces less than double the current.
- This means that the value of V/I rises as the current increases.
- As the current increases, the metal filament gets hotter and the resistance of the lamp rises.

- The graphs for the wire and the lamp are symmetrical.
- The current‑voltage characteristic looks the same, regardless of the direction of the current.