AS Physics 9702 unit 3: Electric Charge 1 UNIT 3 ELECTRIC CHARGE ELECTRIC CIRCUITS: For the current to exist it must have a complete path of conductors. This complete path of conductors is called electric circuit. For example copper wires, which are conductors, are used to connect lamps in a circuit to complete the path for the flow of charges. The battery is also attached to the circuit to push these charges around. To draw on a paper the diagram of complete path of charges is called circuit diagram. It contains symbols for every component of the circuit. Following are some common circuit symbols: There are two different ways of connecting circuit components in a circuit to the same battery. They are called series and parallel circuits. We will discuss about these circuits later in this section. ELECTRIC CHARGE: All matter is made up of atoms. Atoms have three elementary particles that are electrons, protons and neutrons. Since the atom and its particles are very small for us to observe we can understand the presence of these atomic particles by rubbing two polythene rods (an insulator) with woolen cloth. These rods when brought close to each other they repel. It means that rods have acquired an electric charge. There are two types of charges - the positive charge and negative charge. The positive charge is carried by protons or positive ions and negative charge is carried by electrons or negative ions. Following table will describe how different substances behave when rubbed with different materials. Charging an object by rubbing is called electrostatic induction by rubbing or by friction. Material Rubbed with Charge acquired Behaviour Polythene rod Woollen cloth Negative Attract each other Perspex Woollen cloth Positive Ebonite Fur Negative Attract each other Glass Silk positive It must be noted that the charges are not created by rubbing action. When polythene rod is rubbed with a woolen cloth, some of the electrons of the surface atoms of the cloth transferred to the rod and therefore the polythene rod become negatively charged and cloth becomes positively charge. That means that the charges are transferred from cloth to polythene and total charge is always conserved or same. The unit of charge is coulomb or C (capital C). The most common letters used to express charges are Q, q or e. Small e is specifically used for expressing the charge of elementary particle electron (e - ) or proton (e + ).
Prepared by Faisal Jaffer, revised on Jan 2012 ELECTRIC FIELD: 1. It is a field of electric force. 2. An electric field is a space or region around a charged object Q where a stationary positive charge q o experience electric force. 3. It is a vector quantity and its direction is along the direction where the positive charge would move. This means that the electric field is always out from positive charge and in to negative charge. 4. The electric field is represented by the radial straight lines around the charge object. Stronger the field more the number of lines. Electric field intensity or electric field strength of an E electric charge 1. The electric field intensity is defined as force per unit charge. In equation form this is represented as: 2. The unit of electric field intensity is newton per coulomb or N/C. 3. The electric field around charge Q, is considered to be a uniform radial field. This means that a charge q o experiences same force around a charge object Q if it is at equal distance from the centre of the charge at any position. 4. We can plot a graph of electric field intensity E against the distance r from its centre. We can see that the graph shows inverse square law curve that is E inversely proportional to r 2. 5. When two charged plates are placed together, the radial fields of the charges combine to make a uniform electric field. Notice that the field bulges at the ends; generally we ignore this. In this case we can show that the electric field intensity is given by a simpler relationship: 6. E electric field intensity; V potential difference between the two plates and; d - distance between the two plates in meters. In this case the unit of electric field intensity is volts/metre V/m which is same as the other unit that is newton/coulomb N/C. 7. When a charged particle is moving in between the two parallel plates that are carrying opposite charges and have uniform electric field between the plates then the charge particle experience a constant force centripetal perpendicular to the motion of the particle. The deflection of the particle will be towards the opposite charge plate as show in the diagram.
AS Physics 9702 unit 3: Electric Charge 3 Exercise no 3.1: Solve the following questions from past paper. 1. Oct/Nov 2010, Paper 12, questions 28, 29 2. May/Jun 2010, Paper 12, questions 26, 27, 28 3. Oct/Nov 2009, Paper 12, questions 26, 27, 28 4. May/Jun 2009, Paper 1, questions 27, 28, 29 5. May/Jun 2008, Paper 1, questions 30, 31, 6. Oct/Nov 2007, Paper 1, questions 26, 27
Prepared by Faisal Jaffer, revised on Jan 2012 ELELCTIC CURRENT (I): Current (I) is defined as the rate of flow of electric charges (Q) in an electric circuit. The unit of current is ampere (A). Multiple units of ampere are: milli-ampere (ma) = 10-3 A and micro-ampere (μa) = 10-6 A Current is measured by a device called ammeter or multimeter. There are two types of ammeters; analogue and digital. Electric charge (Q) in a conductor is carried by atomic particles electrons or negative ions. Unit of electric charge is coulomb (C). The quantity of electric charge of electron or proton is 1.6 10-19 C. One coulomb is defined as: a charge passing through any point in a circuit when a steady current of 1 ampere maintained for 1 second, that is: 1coulomb (C) = 1ampere (A) 1second (t). Conventional current: The electric current is really a flow of electrons from negative to positive terminal of the battery. However when it was first discovered, scientists wrongly guessed that something that carries charges flows from positive to negative terminal and therefore they describe it as conventional current. Whenever we study electric current and flow of charges we always consider conventional current that is from positive to negative. Direct and alternating currents (d.c. and a.c.): The electrons constantly flowing around the circuit, from the negative terminal of the battery to the positive terminal, produce direct current (d.c). All batteries produce direct current. In mains electricity at homes, the electrons in the circuit move backwards and forwards 50 to 60 times in one second. This kind of current is called alternating current (a.c.). The main advantage of using alternating current over direct current is it can be transmitted from power stations to our homes at very high voltage which reduces the amount energy that is lost during the transmission. Movement of charges in liquids: Electrolysis: Electrolysis is the process in which chemical changes are occur in a conducting liquid when electric charges are passing through it. The conducting liquid is called electrolyte. The word electrolysis means the process of breaking molecules of conducting liquid into its parts (ions) by using electric current. Positive and negative poles of an electric source, such as a battery, can absorb opposite ions of an electrolyte, causing separation of ions and creation of a new substance. Liquid metals are not electrolyte since they can pass current without there being any associated chemical change or making of ions for example in mercury which is liquid. However solution of sodium chloride (NaCl) in water is a good example of electrolyte. Some substances that do not conduct electricity is called non-electrolyte for example sugar-solution.
AS Physics 9702 unit 3: Electric Charge 5 The figure illustrates a simple arrangement of producing electrolysis. The plates by which the current enters and leaves are called electrodes. Electrode connected to the positive terminal of the battery is called anode and an electrode connected to the negative terminal is called cathode. Consider the example of sodium chloride (NaCl) in water as an electrolyte. It contains Na + and Cl - ions which are free to move in water and it conduct electric current. Solid sodium chloride cannot conduct electricity because ions are not free to move but when the current exists through the solution, NaCl splits into Na + and Cl - ions. Sodium ion (Na + ) gains an electron at the cathode and deposit on the surface of the plate and similarly Chlorine ion (Cl - ) losses an electron at anode and deposit on the surface of anode. Movement of charges in solids: Metals: The atomic structures of metals are such that each atom on average has one outer electron which is not required for bonding and which need not to remain attached with its atom. This electron is called free electron or de-localized electron. When the current does not exist these free electrons move randomly in all direction throughout the conductor. When the battery is attached and potential difference is put across the conductor, it produces an electric field and affects the flow of free electrons. It pushes the free electrons towards the positive end of the battery. Thus this creates the flow of charges across the conductor which means electric current. Exercise no 3.2: Solve the following questions from past papers. 1. Oct/Nov 2009, Paper 12, question 33 2. Oct/Nov 2008, Paper 1, question 34 3. Oct/Nov 2007, Paper 1, question 30
Prepared by Faisal Jaffer, revised on Jan 2012 SERIES AND PARALLEL CIRCUITS: Series Circuit: A series circuit is a circuit in which components (eg resistors) are arranged in a chain, so the charges have only one path to follow. The current (rate of flow of charges) is same through each component in series circuit. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors. Equivalent resistance (R) in series circuit can be expressed by. where R 1 and R 2 are the resistances of each resistor. In series circuit the total potential difference (battery voltage) is the sum of individual potential differences (p.d.) across each resistor. That is V = V 1 + V 2 +... where V 1 and V 2 are p.d. across the component R 1 and R 2. The current (I) is same in each resistance therefore the ammeter is connected in series with the other resistances. In series circuit if one component breaks down then the whole circuit will stop working. More the resistance of the component, the higher the potential difference across it. In series circuit the voltage across each resistor divides according to the ratio of resistance value of each resistor. Parallel Circuit: A parallel circuit is a circuit in which the components are arranged such that each component is directly connected to the battery. The parallel circuit makes branches for the current. The current in a parallel circuit breaks up with some current flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel circuit is same. Lesser the resistance in the branch more the current in that branch. Equivalent resistance of each component or resistors R 1 and R 2 in parallel circuit can be expressed by: or In parallel circuit the total current is the sum of individual currents in each branch. I = I 1 + I 2 + Voltage remains same across each resistor that is it has same value as the voltage of the battery. The combine resistance of all resistors in parallel circuit is less than the least resistor in the circuit.
AS Physics 9702 unit 3: Electric Charge 7 POTENTIAL DIFFERENCE: An electric potential difference (V) must exist for current to flow in an electric circuit. It is the work done per unit charge as the charge is moved between two points in an electric circuit. The potential difference (p.d.) between two points in a circuit is 1V if 1J of electrical energy (E) is transferred to another form of energy (i.e. to chargers) when 1 coulomb (C) of charge (Q) passes from one point to another. or Replacing the The equation will be from the definition of charge and current. or Measuring potential difference: A voltmeter is used to measure the electric potential difference between two points in an electric circuit. It is connected in parallel across a resistor in the circuit. It has a very high internal resistance. The unit of potential difference or voltage is volts. OHMS LAW: As the potential difference (V) is increased across a given material (ohmic material or metal) in a circuit, the current (I) flow through the material also increases. or The potential difference (V) between any two points in a conductor is directly proportional to the current (I) through it if the temperature, resistance of the conductor and other conditions are constant. RESISTANCE: where R is the resistance of a conductor. The opposition of to the current in a conductor is called resistance of that conductor. All metals are good conductor of electricity. The best conductor is silver (%) and copper (%) is next to it. All substance have some degree of resistance, there is no substance possible without any resistance and normal temperature. Substances that do not carry current is called insulator. Germanium and silicon have conductivity in between conductors and insulators. They are called semiconductor.
Prepared by Faisal Jaffer, revised on Jan 2012 The unit of resistance is ohm (Greek symbol omega ). One ohm is the resistance when current of one ampere and potential difference of one volt is applied across the resistor. A resistance of a cylinder or wire of certain material: increases if its length (L) increases, increases if its cross-section area (A) decreases, depends upon the type of material ρ where is the resistivity of the conductor which is constant for every material. Measuring resistance: The resistance (R) of a conductor is measured by ohm-meter. Alternatively the resistance of a conductor can be found by setting up the circuit shown in figure and measuring the current (I) and potential difference (V) applied across it. The resistance of the resistor R can be found by the formula. Multiple values of (V) and (I) can be recorded by changing the resistance of a variable resistor. By plotting the graph between V and I and finding the gradient of the line. The gradient is the resistance R. Electromotive force (e.m.f.): In energy terms the e.m.f. is defined as: The energy when converted from any form (chemical or mechanical energy) to electrical energy that it is used to drive one coulomb charge around the complete circuit. This energy per coulomb is called electromotive force or e.m.f. The e.m.f. of a battery is across its terminals when it is not connected to the circuit and it is sometimes called the terminal potential difference. When the circuit is closed, the voltage across the battery falls, because the energy and the voltage of the battery are lost across the internal resistance of battery. To measure e.m.f. or potential difference (p.d.) in a circuit the voltmeter should be connected in parallel. Voltmeter should always have very high internal resistance. Internal resistance of a cell: The p.d. across the terminals of a cell depends on the size of the current being drawn. If no current is being drawn it means the cell is not connected with the circuit then the potential difference between the terminal has its maximum value and know as the electromotive force (e.m.f.) of the cell. This e.m.f. is solely because of the chemical reaction occurring inside the cell. The chemical inside the cell creates a resistance to the current (I). This resistance is called the internal resistance (r) of the cell. When a cell is connected across an external circuit (load R) some of the e.m.f. is used to drive current through the load and rest of the emf drives the same current through the internal resistance. The internal resistance behave as it is in series with the external resistance of the circuit. The equation for the two resistance connected in series is
AS Physics 9702 unit 3: Electric Charge 9 or or where Ir is the p.d. across the internal resistance and V is the potential difference across the external resistance. From equation when I=0 it means that the cell is not connected to any external resistance then V=E the emf of the cell. Measurement of e.m.f. and internal resistance of a cell: 1. Connect the circuit as shown in the diagram. 2. Record six readings of voltmeter (V) and ammeter (I) of the cell by changing the values of variable resistance R. 3. The resistance of the voltmeter should be higher than the combine resistances of r and R. 4. Plot the graph between V (on y-axis) and I (on x-axis) and draw the best fit straight line. The equation of the straight line should be. 5. Compare the straight line equation with the equation of e.m.f. or by rearranging. 6. Comparing these two equations shows gradient of the line m is r and y-intercept c is E, the e.m.f. of the battery. 7. The internal resistance of a typical 1.5V cell is 1Ω if the current is limited to 0.2A, the terminal PD will range from 1.5V when I= 0 to 1.3V when I=0.2A. Maximum power delivered by the cell: Consider the circuit diagram shown in the figure in which the e.m.f. of the cell is E, the internal resistance is r and driving current is I through a load of resistance R. The power delivered by the cell to resistance R is but we know that therefore by replacing The maximum power dissipated by cell is when R=r. A given source of e.m.f. delivers maximum amount of power to a load when the resistance of the load is equal to the internal resistance of the source. Exercise no 3.3: Solve the following questions from past papers. 1. Oct/Nov 2007, Paper 1, question 29 2. Oct/Nov 2009, Paper 12, question 30 3. Oct/Nov 2010, Paper 22, question 6 4. Oct/Nov 2009, Paper 21, question 6 5. Oct/Nov 2009, Paper 22, question 6 6. Oct/Nov 2009, Paper 22, question 6 7. May/June 2008, Paper 1, question 38 8. May/June 2010, Paper 22, question 6(a) 9. May/June 2008, paper 2, question 6 10. May/June 2007, paper 2, question 6
Prepared by Faisal Jaffer, revised on Jan 2012 I-V Characteristic of various components: Metal: Metal conductors obey ohm s law, provided their temperature does not change or we can say that the metal conductors have constant resistance provided its temperature is constant. The I-V graph between current (I), on y-axis (dependent variable) and voltage (V) on x-axis (independent variable) is straight line. Diode: In semiconductor diode it allows the current only in one direction and that is forward bias connection. In diode the current is not proportional to voltage (or PD) applied because when the PD is reversed, the current is almost zero. This is reverse biased connection. Filament: In tungsten filament as the current increases, the temperature also rises and the resistance goes up. So the current is not proportional to PD. This happens because as the current increases in the filament the temperature also increases which increase the resistance of the conductor and decrease the flow of charges in the conductor.
AS Physics 9702 unit 3: Electric Charge 11 Thermistor: A thermistor is a heat sensor (resistor) which changes its resistance with the change of temperature (heat) around it. Its resistance decreases as the temperature increases which is reverse to the normal conductor. For example: Icy water 0 C has high resistance, about 12kΩ. Room temperature 25 C has medium resistance, about 5kΩ. Boiling water 100 C has low resistance, about 400Ω. Thermistor is called input transducer. It means it changes its resistance with the change in environment. The I-V graph of a thermistor is not a straight line and therefore it does not obey Ohm s law. As more current is through the thermistor the graph gets steeper. The thermistor is a semiconductor and conducts more electricity when heated. This is because as the temperature increases the thermistor makes available more free electrons to carry current. Therefore as the current increases the thermistor get hotter and releasing more electrons resulting in a reduction in resistance. LDR (Light Dependent Resistor): An LDR is a light sensor (resistor) which changes its resistance with the brightness of light around it. It is made from cadmium sulphide compound (CdS) and its resistance decreases as the brightness of light falling on the LDR increases. Darkness: maximum resistance, about 10 6 Ω. Very bright light: minimum resistance, about 100Ω. LDR is called input transducer. It means it changes resistance with the change in environment. The I- V graph is a straight line. When light shines on it releases electrons which increases the number of electrons to carry the current. Thus, as the light increases the current increases resulting in a reduction in resistance. In dark however no extra electrons are available so the current experiences a greater resistance.
Prepared by Faisal Jaffer, revised on Jan 2012 ELECTRIC POWER: Rate of doing work is called power. It is define as replacing replacing Unit of power is watts (W) and larger units are 1 kilowatt (kw) = 1000 W and 1megawatt (MW) = 1000 000 W. The power of electrical appliances can be calculated by multiplying the current (I) passing through it by the potential difference (V) across it. Exercise no 3.4: Solve the quiz on the website http://www.learnabout-electronics.org/resistors_23.php Solve the following questions from past papers. 1. May/June 2008, Paper 2, question 6 2. Oct/Nov 2007, Paper 1, question 29
AS Physics 9702 unit 3: Electric Charge 13 KIRCHHOFF S LAW: Kirchhoff s first law Junction rule - Conservation of charge: At junction in a circuit, the total current entering is equal to the total current leaving it. Mathematically ΣI=0 In figure at junction A current I 1 and I 2 are approaching and current I 3 is leaving therefore. Kirchhoff s second law Loop rule - Conservation of energy: In any closed loop in a circuit, the sum of the e.m.f. (E) must be equal to the sum of all the IR products. Mathematically ΣE = ΣIR In the circuit in e.m.f. of V 1 is E 1 and e.m.f. of V 2 is E 2. Considering the loop 1 clockwise then the equation can be written as for loop 2 anticlockwise and for loop 3 Substituting the values and solving the three equations simultaneously we can find the values of I 1, I 2 and I 3. Rules for applying Kirchhoff s Law: 1. Draw an arrow to show the direction of current in each branch of the circuit. Choose any direction clockwise or anticlockwise. If you chose the wrong direction then the value of current will turn out to be negative. 2. Mark each resistor with a plus sign at one end and minus sign at the other end, in a way that is consistent with the direction of current chosen in step 1. Mark each battery such that the positive terminal considered as higher potential and negative terminal considered as lower potential. Conventional current always flow from higher potential to lower potential. 3. While calculating the current through a battery the internal resistance is considered as separate resistance. 4. Apply first and second rule to the circuit and obtained as many independent equations as many number of variables. 5. Solve the equations simultaneously for the known variables. Exercise no 3.5: Solve the following questions from past papers. 1. Oct/Nov 2007, Paper 1, question 29 2. May/June 2010, Paper 22, question 6(a) 3. May/June 2009, paper 22, question 7 4. May/June 2009, paper 21, question 7
Prepared by Faisal Jaffer, revised on Jan 2012 POTENTIAL DIVIDER OR VOLTAGE DIVIDER A potential (or voltage) divider is combination of two resistors, as shown in the figure. The output voltage V2 from a potential divider will be a proportion of the input voltage V1 and is determined by the ratio of the two resistance values. In the arrangement of the circuit in the diagram the value of V2, the output voltage can be determine by the formula: V1 is the input voltage and R1 and R2 are the resistor in series. This arrangement is normally used to change voltage across a circuit component, for example to change the brightness of the lamp, or control the volume (loudness) in a hi-fi amplifier circuit. Potential divider and LDR: Now what happend when one of the resistors is replaced with LDR, the light dependent resistor. The resistance of LDR decreases as more light falls on it. It means that there will be low p.d. across R2 and high p.d. across R1. If a lamp is connected across R1 then the brightness of the lamp increases when the intensity of light falling on LDR decreases. Voltage divider circuit gives an output voltage which changes with illumination of the surrounding. Potential divider and thermistor: We can consider the similar situation by replacing thermistor with the R2 in the circuit. The resistance of thermistor decreases as the temperature rises. They are called negative temperature coefficient, or ntc thermistors. A typical ntc thermistor is made using semiconductor metal oxide materials. Semiconductors have resistance properties midway between those of conductors and insulators. As the temperature rises, more charge carriers become available and the resistance falls. If we connect a lamp across the resistance R1, then the brightness of the lamp increases if the temperature of the surrounding increases. Exercise no 3.6: Solve the following questions from past papers. 1. Oct/Nov 2007, Paper 1, question 29 2. May/June 2008, Paper 1, questions 36, 37 3. Oct/Nov 2007, Paper 1, questions 32, 33 4. May/June 2010, Paper 22, question 6(a)
AS Physics 9702 unit 3: Electric Charge 15 Comparing the E.M.F.s of two cells: A potentiometer can be used to compare the e.m.fs of two cells. Consider the circuit below. A resistance wire of length one meter is connected with a cell called the driver cell that will remain unchanged. Connect the cell X, of known E.M.F., with the circuit and find the null point on the centre deflection ammeter by bringing in the sliding contact with the resistance wire. Measure the length of resistance wire as L X (example 0.70m). Repeat the same procedure by connecting the battery Y of unknown EMF in the circuit and find the length of wire as L Y (example 0.90m). The ratio of the two e.m.fs is equal to the ratio of their lengths of resistance wire. Exercise no 3.7: Solve the following questions past papers. 1. May/June 2008, Paper 1, question 38 2. Oct/Nov 2007, Paper 1, question 34 Comparing Electric and Gravitational Fields There are many analogies that can be drawn between electric fields and gravitational fields. Theoretical physicists would go as far as saying that the two are possibly different expression of the same thing. Let us compare the two: Feature Electric Field Gravity Field Exert force on Positive or negative charge Mass Constant of Proportionality G where 0 is the permittivity of free space. The value of can be changed by adding a material. The value of G, the universal gravity constant has the same value for all media, including a vacuum. Relationship with distance r Inversely proportional to r 2. Inversely proportional to r 2. Force Equation Nature of force Acceleration in uniform field Can be attractive or repulsive and goes from positive to negative charge or Always attractive pointing towards the centre of the earth Relative strength Strong at close range Weak. Can only be felt when the objects are massive Range Infinite Infinite The gravitational attraction between particles in an atom is so small and considered negligible. The nucleus and its electrons are held together entirely by electrostatic forces, and these are involved in chemical reactions. Gravity forces hold planets together and hold them in their orbits. Electrostatic forces over the interplanetary distances can be ignored.
Prepared by Faisal Jaffer, revised on Jan 2012 Charge to mass ratio of electron The mass of an electron is 9.11 x 10-31 kg, and its charge is 1.602 10-19 C. These quantities are too small to directly measure, even if you were somehow able to isolate a single electron in the laboratory. However, using principles of electromagnetism, indirect measurements of the charge and the mass of the electron can be accomplished. These indirect measurements will be accomplished by taking advantage of quantities that are directly measurable in the laboratory setting. These direct quantities will be derived from knowledge of the velocity of an electron moving in a magnetic field. Consider an electron of charge e is passing in between the two parallel plates of potential difference V. The direction of electric field is perpendicular to the direction of motion of electron. Electron creates a curved (trajectory path) attracting towards the positive plate. The electric potential energy lost by electron is The kinetic energy gain by the electron at any particular instance is given by As the electron is accelerating in the electric field it loses its electric potential energy and gains the kinetic energy (a similar analogy as an object is falling towards the earth in gravitational field). Equate the two energies. Rearranging the equation V the p.d. across the two plates can be recorded from the battery voltage and speed of the electron can be calculated from the distance travelled by the electron in between the two plates (that is length of the plates) and time taken. The charge to mass ratio e/m is also called the specific charge of electron. Electron-volt: It is the energy required to accelerate an electron through a potential difference of one volt. Replacing the quantity of charge as e = 1.6 10-19 C and potential difference as 1 volt in equation This implies that 1ev=1.6 10-19 joules It is a convenient energy unit, particularly for atomic and nuclear processes. It is the energy given to an electron by accelerating it through 1 volt of electric potential difference.