Topic 5
Electric Currents /
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 C1), or the volt (V). Like gravitational potential it is a scalar quantity.
In the figure below, 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 below shows some values of the electric potential at points in the electric field of a positivelycharged 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 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 = qV and the charge on an electron or proton is 1.6 x 10-19C
Then W = 1.6 x 10-19C x 1V =1.6 x 10-19 J
Therefore 1 eV = 1.6 x 10-19 J
Conduction in Metals
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.
What happens when a battery is attached to the copper wire? 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.
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 1019 C.
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.
TOK
Why do models change as knowledge changes (current vs electron flow)?
Resistance
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
Resistors are components that are made to have a certain resistance. They can be made of a length of nichrome wire.
Factors Affecting Resistance
Resistance depends on; Temperature, Material of conductor, Length, Cross-sectional area
Temperature
The resistance of a metallic conductor increases as the temperature increases e.g. copper. The resistance of a semiconductor/insulator decreases as the temperature increases e.g. thermistor.
Length
Resistance of a uniform conductor is directly proportional to its length.
i.e. R µ L
Cross-sectional area
Resistance of a uniform conductor is inversely proportional to its cross-sectional area.
i.e. R µ 1
A
Material
The material also affects the resistance of a conductor by a fixed amount for different materials. This is known as resistivity (r).
R = rL r = constant of proportionality
A Unit: ohm meter W m
r = Rpd 2 (For a wire with circular cross-sectional area)
4L
Resistance & Resistivity
The resistance of a conductor is directly proportional to the length since the current needs to pass through all the atoms in the length. The resistance is inversely proportional to the cross-sectional area since there is more room for the current to pass through. The above observations can be combined and the resistance, R of the conductor is
Resistivity is an inherent property of a material, inherent in the same sense that density is an inherent property.
Ohm’s Law
The current through a metal wire is directly proportional to the p.d. across it (providing the temperature remains constant).
Materials that obey Ohm's law are called ohmic conductors.
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: I is 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.
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 currentvoltage characteristic looks the same, regardless of the direction of the current.
TOK
How can we be sure about relationships between measured quantities?
Power Dissipation
P= W/t
W = qV
q = It or t = q/I
Therefore P = qV/(q/I)
P = VI
Using V = IR & P = VI
P = IR x I
P = I2R
Or as I = V/R
P = V x V/R
P = V2/R
P = VI = I2R = V2/R
Electromotive Force
Defining potential difference
The coulombs entering a lamp have electrical potential energy Those leaving have very little potential energy. There is a potential difference (or p.d.) across the lamp, because the potential energy of each coulomb has been transferred to heat and light within the lamp. p.d. is measured in volts (V) and is often called voltage.
The p.d. between two points is the electrical potential energy transferred to other forms, per coulomb of charge that passes between the two points.
Resistors and bulbs transfer electrical energy to other forms, but which components provide electrical energy? A dry cell, a dynamo and a solar cell are some examples. Any component that supplies electrical energy is a source of electromotive force or e.m.f. It is measured in volts. The e.m.f. of a dry cell is 1.5 V, that of a car battery is 12 V. A battery transfers chemical energy to electrical energy, so that as each coulomb moves through the battery it gains electrical potential energy. The greater the e.m.f. of a source, the more energy is transferred per coulomb. In fact:
The e.m.f of a source is the electrical potential energy transferred from other forms, per coulomb of charge that passes through the source.
Compare this definition with the definition of p.d. and make sure you know the difference between them.
Internal Resistance
The cell gives 1.5 joules of electrical energy to each coulomb that passes through it, but the electrical energy transferred in the resistor is less than 1.5 joules per coulomb and can vary. The circuit seems to be losing energy can you think where? The cell itself has some resistance, its internal resistance. Each coulomb gains energy as it travels through the cell, but some of this energy is wasted or `lost' as the coulombs move against the resistance of the cell itself. So, the energy delivered by each coulomb to the circuit is less than the energy supplied to each coulomb by the cell. Very often the internal resistance is small and can be ignored. Dry cells, however, have a significant internal resistance. This is why a battery can become hot when supplying electric current. The wasted energy is dissipated as heat.
Resistance Combinations
Series
The diagram above shows three resistors connected in series. There are 3 facts that you should know for a series circuit:
the current through each resistor in series is the same
the total p.d., V across the resistors is the sum of the p.d.s across the separate resistors, so: V = Vl + V2 + V3
the combined resistance R in the circuit is the sum of the separate resistors
R = Rl + R2 + R3
Suppose we replace the 3 resistors with one resistor R that will take the same current I when the same p.d. V is placed across it
This is shown in the diagram above. Let's calculate R. We know that for the resistors in series:
V = Vl + V2 + V3
But for any resistor: p.d. = current x resistance (V = I R). If we apply this to each of our resistors, and remember that the current through each resistor is the same and equal to I, we get:
IR = IRl+IR2+IR3
If we now divide each term in the equation by I, we get:
R = R1 + R2 + R3
Disadvantages of Series Circuits?
When one component fails the whole circuit fails.
The current is the same at all points and the
voltage is divided between the bulbs.
The more bulbs added the dimmer each one is.
Resistors in Parallel
We now have three resistors connected in parallel. There are 3 facts that you should know for a parallel circuit:
the p.d. across each resistor in parallel is the same
the current in the main circuit is the sum of the currents in each of the parallel branches, so: I = I1 + I2 + I3
the combined resistance R is calculated from the equation:
Suppose we replace the 3 resistors with one resistor R that takes the same total current I when the same p.d. V is placed across it.
This is shown in the diagram above. Now let's calculate R. We know that for the resistors in parallel: I = I1+I2+I3 But for any resistor, current = p.d. = resistance (I = V/R ). If we apply this to each of our resistors, and remember that the p.d. across each resistor is the same and equal to V, we get:V/R=V/R1 + V/R2 + V/R3 Now we divide each term by V, to get:
1/R=1/R1 + 1/R2 + 1/R3
You will find that the total resistance R is always less than the smallest resistance in the parallel combination.
Advantages of the Parallel Circuit?
When one bulb fails the rest of the circuit continues to work.
The more components, the lower the resistance.