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Current of Electricity Notes

Current of Electricity

A. Content

  • Conventional Current and Electron Flow
  • Electromotive Force
  • Potential Difference
  • Resistance

B. Learning Outcomes

  • Students should be able to:
    • (a) state that current is a rate of flow of charge and that it is measured in amperes
    • (b) distinguish between conventional current and electron flow
    • (c) recall and apply the relationship charge = current x time to new situations or to solve related problems
    • (d) state that electromotive force (e.m.f.) of a source is the work done per unit charge by the source in driving charges around a complete circuit and that it is measured in volts
    • (e) calculate the total e.m.f. where several sources are arranged in series
    • (f) state that the potential difference (p.d) across a component in a circuit is the work done per unit charge in driving charges through the component and it is measured in volts
    • (g) state that resistance = p.d. / current
    • (h) apply the relationship R = V/I to new situations or to solve related problems
    • (i) recall and apply the relationship of the proportionality between resistance and the length and cross-sectional area of a wire to new situations or to solve related problems
    • (j) describe the effect of temperature increase on the resistance of a metallic conductor
    • (k) sketch and interpret the I-V characteristic graphs for a metallic conductor at constant temperature (ohmic conductor), for a filament lamp and for a semiconductor diode

C. References

  • Chew, C., Chow, S. F. and Ho, B. T. Physics Matters for GCE ‘O’ Level (4th Edition). Marshall Cavendish Education.
  • Chew C., Ho B.T., Low B.Y., Yeow K.H. (2023). GCE ‘O’ Level: Physics Matters (5th ed). Marshall Cavendish Education. Chapter 16: Current of Electricity.

D. Notes Outline

  • Introduction – Electric Current
  • Electromotive Force and Potential Difference
  • Resistance

1. INTRODUCTION - ELECTRIC CURRENT

  • (a) state that current is a rate of flow of charge and that it is measured in amperes
  • (c) recall and apply the relationship charge = current x time to new situations or to solve related problems
  • Electricity is the set of physical phenomena associated with the presence and flow of electric charge.
  • Current, I: Rate of flow of electric charge (through a given section of an electrical conductor).
  • I = \frac{Q}{t} where
    • I: current (ampere, A)
    • Q: electric charge (coulomb, C)
    • t: time (second, s)
  • Example: A current of 3A flows in a circuit for 2 minutes. What is the total charge flowing in the circuit?

1.1. CONVENTIONAL CURRENT FLOW AND ELECTRON FLOW

  • (b) distinguish between conventional current and electron flow
  • While we know that current is the rate of flow of electric charge, it is important to note that there is both conventional current flow and electron flow.
  • Conventional current flow is the direction in which positive charges will flow, while electron flow is the direction in which electrons will flow. The directions of conventional current flow and electron flow are opposite of each other.
  • Conventional current and electron flow:
    • Electrons are moving from the negative terminal to the positive terminal
    • Conventional current is flowing from the positive terminal to the negative terminal

1.2. MEASURING CURRENT

  • An instrument that can be used to measure the amount of current flowing through the circuit is the ammeter.
  • The ammeter should be connected in series to the rest of the circuit and the current should flow into the ammeter through the positive (red) terminal and leave via the negative (black) terminal.
  • Ammeters are assumed to possess an infinitely small amount of resistance which implies that all current will flow through it, and the addition of an ammeter into a circuit does not change the current flowing in the circuit.

1.3. CIRCUIT DIAGRAMS

  • Circuit symbols have been created for many common electrical components to ease the process of drawing circuit diagrams.

2. ELECTROMOTIVE FORCE (E.M.F.) AND POTENTIAL DIFFERENCE

  • Voltage can refer to either electromotive force of a source (e.m.f.) or potential difference across an electrical component in a circuit (p.d.).

2.1. ELECTROMOTIVE FORCE (E.M.F.)

  • (d) state that electromotive force (e.m.f.) of a source is the work done per unit charge by the source in driving charges around a complete circuit and that it is measured in volts
  • Electromotive force (e.m.f.), E or ε (of an electrical source): Work done per unit charge by a source in driving charges around a complete circuit.
  • E = \frac{W}{Q} where
    • E: e.m.f. (volt, V)
    • W: work done by the source (joule, J)
    • Q: charge (coulomb, C)
  • From the definition, e.m.f. is the energy transferred electrically by one coulomb of charge that passes through the source, i.e. the charges must have gained energy to move through the whole circuit.
  • Sources of e.m.f. include a cell. A series of cells is called a battery.
  • Example: The e.m.f. of a cell is 4.0 V. Calculate the energy dissipated by the cell if it drives 8.0 C of charge round the circuit.
  • Example: The e.m.f. of a cell is 4.0 V. Calculate the total energy dissipated by the cell in 20 seconds if a current of 2.0 A flows in the circuit.

2.2. POTENTIAL DIFFERENCE (P.D.)

  • (f) state that the potential difference (p.d) across a component in a circuit is the work done per unit charge in driving charges through the component and it is measured in volts
  • Potential difference (p.d.), V (across a component in an electric circuit): Work done per unit charge in driving charges through a component.
  • V = \frac{W}{Q} where
    • V: p.d. across the component (volt, V)
    • W: work done in driving the charge through the component (joule, J)
    • Q: charge flowing through the component (coulomb, C)
  • When the potential difference across a component is 1.0 V, 1.0 J of energy is transferred electrically per 1.0 C of charge that flows through the component.
  • Example: If a charge of 3.75 x 10^4 C flows through an electric heater and the amount of energy transferred electrically to increase energy in the internal store of the heater is 9.0 MJ, calculate the potential difference across the ends of the heater.

2.3. MEASURING E.M.F. AND P.D.

  • A voltmeter is used to measure both e.m.f. and p.d.
    • The positive and negative terminals of the voltmeter are connected to the positive and negative terminals of the cell respectively.
    • The voltmeter is always connected in parallel across the component.
  • Voltmeters are assumed to possess a very large amount of resistance which implies that almost no current will flow through it. Hence, when a voltmeter is connected in parallel across a branch of a circuit, it does not change the current flowing through that branch.

2.4. CELL ARRANGEMENT AND E.M.F.

  • (e) calculate the total e.m.f. where several sources are arranged in series
  • Arranging dry cells in series or parallel will affect the resultant e.m.f. of the circuit.
  • Series
    • Resultant e.m.f.: Sum of all cells arranged in series (e.g. 1.5 V + 1.5 V = 3.0 V)
    • Life span of cells: Shorter
    • Reason: The charges transfer chemical potential energy from each cell electrically to other circuit components as they pass through them.
  • Parallel
    • Resultant e.m.f.: Equal to that of a single cell (e.g. 1.5 V)
    • Life span of cells: Longer
    • Reason: The charges transfer only a portion of the chemical potential energy from each cell electrically to other circuit components as they pass through them.

3. RESISTANCE

  • (g) state that resistance = p.d. / current
  • (h) apply the relationship R = V/I to new situations or to solve related problems
  • Resistance, R: Ratio of potential difference across a component to the current flowing through it.
  • R = \frac{V}{I} where
    • R: resistance of the component (ohm, Ω)
    • V: p.d. across the component (volt, V)
    • I: current flowing through the component (ampere. A)
  • It is also the measure of the opposition an electric current experiences when it flows through the component i.e. it determines the magnitude of the current flowing through the circuit.
  • 1 Ω is the resistance of a conductor through which a current of 1 A flows when a potential difference of 1 V is maintained across it.

3.1. RESISTORS

  • The current in a circuit can be varied by changing the resistance of the circuit. This can be done using resistors.
  • Resistors are conductors that can be used to control the size of current in the circuit. There are two types of resistors, namely fixed resistors and variable resistors.
  • For a fixed resistor the actual resistor value is indicated by the colour bands.

3.2. OHM’S LAW (YOU ARE NOT REQUIRED TO STATE OHM’S LAW)

  • Ohm’s Law: The current flowing through a metallic conductor is directly proportional to the potential difference applied across its ends, provided that the physical conditions (such as temperature) are constant.
  • I ∝ V
  • Ohm’s Law was discovered by Georg Ohm in 1826.

3.2.1. OHMIC CONDUCTORS

  • (j) describe the effect of temperature increase on the resistance of a metallic conductor
  • (k) sketch and interpret the I-V characteristic graphs for a metallic conductor at constant temperature (ohmic conductor), for a filament lamp and for a semiconductor diode
  • Conductors that obey Ohm’s Law are known as ohmic conductors. Conversely, those that do not obey Ohm’s Law are non-ohmic conductors.
  • The I-V graph of an ohmic conductor at constant temperature
    • is a straight line that passes through the origin;
    • has a constant gradient that is equal to the inverse of the resistance R of the conductor.
    • Since \frac{V}{I} = constant, R = constant
  • In general, the resistance of metallic conductors (ohmic and non-ohmic) increases with temperature.
  • Example: What is the resistance of the wire?

3.2.2. NON-OHMIC CONDUCTORS

  • (k) sketch and interpret the I/V characteristic graphs for a metallic conductor at constant temperature (ohmic conductor), for a filament lamp and for a semiconductor diode

3.2.2.1. FILAMENT LAMP

  • The I-V characteristic graph for a filament lamp is a curve. This indicates that current I is not proportional to potential difference V. For example, when V is doubled, I is less than doubled.
  • The ratio of \frac{V}{I} increases as p.d. increases. Since \frac{V}{I} = R, the resistance increases as p.d. increases. Thus, filament lamps do not obey Ohm’s law and are non-ohmic conductors.

3.2.2.2 DIODE

  • The I-V characteristic graph for a (semiconductor) diode is a curve. This indicates that current I is not proportional to potential difference V. Thus, a diode does not obey Ohm’s law and is a non-ohmic conductor.
  • Using the diagram above as an example:
    • In the forward direction (V is positive), current increases very rapidly when potential difference > 0.6 V. Thus, the diode has a very low resistance when p.d. > 0.6 V. The diode is said to be forward-biased.
    • In the reverse direction (V is negative), the current is negligible and the diode has a very high resistance. The diode is said to be reverse-biased.
  • The current flows through the diode effectively in one direction only.

3.3. MEASURING RESISTANCE

  • The resistance of a component can be determined through experimentation.
    1. Set up the apparatus according to the circuit diagram.
    2. Adjust the variable resistor to allow the smallest possible current to flow in the circuit.
    3. Note the ammeter reading I and voltmeter reading V.
    4. Adjust the variable resistor to allow a larger current to flow in the circuit. Again, note the values of I and V.
    5. Repeat the above for five sets of I and V readings.
    6. Plot a graph of V against I, and determine the gradient of the graph.
    7. The gradient of the graph gives the resistance of the load, R.
  • (Note: As the resistor is an ohmic conductor, the ratio of V against I is actually the gradient of the graph, as the graph will pass through the origin. For non-ohmic conductors, the resistance when a certain p.d. is applied across them is given by the ratio of V against I, NOT by the gradient of the graph.)

3.4. RESISTIVITY, ρ

  • (i) recall and apply the relationship of the proportionality between resistance and the length and cross-sectional area of a wire to new situations or to solve related problems
  • There are several factors affecting resistance:
    1. Temperature: The higher the temperature, the higher the resistance.
    2. Length of the conductor, l: The longer the wires, the higher the resistance i.e. R α l
    3. Cross-sectional area of conductor, A: The thinner the wires, the higher the resistance i.e. R α A
    4. Type of conductor i.e. resistivity, ρ: Resistivity depends on the material. The larger the resistivity, the higher the resistance of the material i.e. R α ρ
  • If the temperature is kept constant, the resistance of a conductor is dependent on:
    1. its length, L
    2. its cross-sectional area, A
    3. its resistivity i.e. type of material,
  • R = ρ \frac{L}{A} where
    • L: length of the conductor perpendicular to the cross-sectional area A (m)
    • A: cross-sectional area of the conductor (m^2)
    • ρ: resistivity of the material (Ω m)