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3.5.1 Current electricity

3.5.1.1 Basics of electricity

Charge

  • Measured in coulomb (C)
  • Charge of 1 electron = \(-1.60 \times 10^{-19} \text{ C}\)
  • Scalar quantity

Electric current (I)

  • The rate of flow of charge
  • \(I = \frac{\Delta Q}{\Delta t}\)

Potential difference (V)

  • The energy transferred per unit charge between two points in a circuit
  • When a charge of 1 C passes through a p.d. of 1 V, it does 1 J of work
  • \(V = \frac{W}{Q}\)

Resistance (R)

  • A measure of how difficult it is for charge carriers to pass through a component
  • \(R = \frac{V}{I}\)

Capacity

  • A measure of the total amount of charge which the battery can push around a circuit
  • Commonly measured in ampere-hours (A h)
  • 1 Ah = a current of 1 A can flow for 1 hour = 3600 C

Types of charge carriers

  • Insulator
    • Each electron is attached to an atom and cannot move away from the atom
  • Metallic conductor
    • Most electrons are attached to metal ions but some are delocalised
    • Delocalised electrons can carry charge through the metal
    • When a voltage is applied across the metal these conduction electrons are attracted towards the positive terminal of the metal
  • Semiconductor
    • Number of charge carriers increase with an increase of temperature (electrons break free from the atoms of the semiconductor)
    • Resistance fall as temperature rise

3.5.1.2 Current-voltage characteristics

Ohm's law

  • The current through a conductor is directly proportional to the potential difference across the conductor provided that temperature and other physical conditions remain constant
  • \(V = IR\)
  • Not the definition of voltage

Types of different conductors

  • Ohmic conductor
    • Follows Ohm’s law
    • Constant resistance as long as temperature and other physical conditions remain constant
    • Current-voltage graph will look like a straight line through the origin
    • Exported image|516x183
  • Semiconductor diode
    • Only lets current flow in one direction, converts AC to DC
    • Forward biased: allow current to flow easily past the threshold voltage (smallest voltage needed to allow current to flow)
    • Reverse biased: the resistance of the diode is extremely high so that only a very small current can flow
    • Exported image|481x165
  • Non-ohmic conductors e.g. filament lamp
    • Ohm's law obeyed initially (a straight line initially)
    • Does not have a constant resistance
    • As voltage increases current increases
    • More electrons flow through the wire per second
    • Current heats filament
    • Higher rate of collisions between ions in the lattice structure and electrons
    • Conducting electrons slow down more and lose more kinetic energy so current falls and resistance increases
    • Rate of increase of current is less than if resistance was constant
    • As current or voltage increases resistance increases so the gradient is not constant
    • Negative voltage and current produces the same effect
    • Exported image|463x165

Assumptions

  • Assume ammeters and voltmeters are ideal unless otherwise stated
  • Ammeters can be assumed to have zero resistance
  • Voltmeters can be assumed to have infinite resistance

3.5.1.3 Resistivity

Resistivity (\(\rho\))

  • Resistance per unit length \(\times\) area of cross section
  • \(\rho = \frac{RA}{L}\) or \(R = \frac{\rho L}{A}\)
  • Unit = \(\Omega \text{m}\)

Effect of temperature on the resistance of metal conductors

  • When the temperature of a metal conductor increases its resistance will increase
  • Metal ions gain KE from heating and vibrate more so they take up more space
  • More collisions between electrons and metal ions per second so they slow down more
  • Current falls so resistance increases

Effect of temperature on the resistance of thermistors

  • When the temperature of a thermistor increases, its resistance will decrease
  • Increasing the temperature of a thermistor causes electrons to be emitted from atoms = more charge carriers = current increase
  • Exported image|296x207

Application of thermistors

  • Temperature sensors
    • Trigger an event to occur once the temperature drops below or reaches a certain value
    • e.g. turn on the heating once room temperature drops below a specific value

LDR

  • Resistance decreases as light intensity increases
  • Used to trigger certain events
  • P7 F Thermistors LDRs Edexcel Physics Elevise|314x202

Superconductivity

  • A property of certain materials which have zero resistivity at and below a critical temperature (\(T_{c}\)) which depends on the material
  • Resistivity decreases as temperature decreases
  • Zero resistivity = zero resistance
  • Critical temperature normally extremely low (close to 0 K)
  • SUPERCONDUCTIVITY

Applications of superconductors

  • Power cables
    • Reduce energy loss due to heating to zero during transmission
  • Production of strong magnetic fields
    • Do not require a constant power source
    • Used in maglev trains / certain medical applications

Resistance of a wire

  • Normally assumed to be 0 so no PD is lost between 2 points on a wire with no resistors between them
  • The assumption can break down if the current is high / resistance in the rest of the circuit is low

Required practical 5 - determining wire resistivity

Method

  • Set up the circuit as shown
    • Exported image
  • Connect the flying lead to the wire so that 0.10 m of the wire has its resistance measured
  • Switch on the power supply and adjust the voltage of it so that the current in the circuit is 0.50 A
  • Turn off the power supply between readings so the wire does not heat up and increase in resistance
  • Measure and record the length and voltage across the wire by taking reading on the voltmeter
  • Move the flying lead to increase the length by 0.10 m and repeat the measuring process for lengths up to 1.00 m
  • Repeat the experiment twice for each reading and calculate an average voltage at each length
  • Calculate resistance at each length by \(R = \frac{V}{I}\)
  • Plot a graph of resistance against length
  • Resistivity = gradient \(\times\) cross sectional area (gradient = \(\frac{\rho}{A}\))

Errors

  • Random Errors
    • The current flowing through the wire will cause its temperature to increase and increase its resistance and resistivity
      • Only allow small currents to flow through the wire so the temperature is kept constant and low
      • The power supply should be switched off between readings so its temperature doesn't change its resistance
    • Make at least 5-10 measurements of the diameter of the wire with the micrometer screw gauge and calculate an average diameter to reduce random errors in the reading
    • The wire should be free from kinks and held straight so the measurement of the length is as accurate as possible.
  • Systematic errors
    • Zero error when measuring wire length

Safety Considerations

  • When there is a high current, and a thin wire, the wire will become very hot
  • Make sure never to touch the wire directly when the circuit is switched on
  • Switch off the power supply right away if you smell burning
  • Make sure there are no liquids close to the equipment, as this could damage the electrical equipment

3.5.1.4 Circuits

Circuit symbols

  • Exported image

Series circuit properties

  • The current is the same at all points
    • Exported image
    • ① = ② = ③
  • The sum of potential differences across the components is equal to the total EMF of the power supply
    • Exported image
    • ① = ② + ③

Parallel circuit properties

  • The current splits up
    • Some of it going one way and the rest going the other
    • Total current in the circuit = sum of the currents in the branches
    • Exported image
    • ① = ② + ③ = ④
  • Total voltage of a parallel circuit has the same value as the voltage across each branch
    • Exported image
    • ① = ② = ③ + ④

Total voltage of cells

  • Cells joined in series
    • \(V_{T} = V_{1} + V_{2} + V_{3} + \ldots\)
  • Identical cells joined in parallel
    • Total voltage = voltage of one cell as current is split equally between branches so overall pd is the same as if the total current was flowing through a single cell
    • \(V_{T} = V_{1} = V_{2} = V_{3} = \ldots = \epsilon - \frac{Ir}{n} = \text{emf} - \frac{\text{total current of the circuit} \times \text{internal resistance of each cell}}{\text{number of cells}}\)
    • Total internal resistance = calculated in the same way as other parallel circuits
    • Act like one cell but with reduced internal resistance

Advantages of cells joined in parallel

  • Reduce the combined internal resistance of the cells - reduce lost volts
  • Less power drawn from each cell so it lasts longer

Total resistance calculation

  • In series
    • \(R_{T} = R_{1} + R_{2} + R_{3} + \ldots + R_{n}\)
  • In parallel
    • \(\frac{1}{R_{T}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \ldots + \frac{1}{R_{n}}\)

Power (\(P\)) and energy (\(E\))

  • \(P = IV = \frac{V^{2}}{R} = I^{2}R\)
  • \(E = Pt = IVt\)

Kirchhoff's laws

  • In DC circuits
  • Kirchhoff's first law (conservation of charge)
    • The total current flowing into a junction is equal to the current flowing out of that junction
    • No charge is lost at any point in the circuit
  • Kirchhoff's second law (conservation of energy)
    • The sum of all the voltages in a series circuit is equal to the battery voltage
    • No energy is lost at any point in a circuit

3.5.1.5 Potential divider

Potential divider

  • Circuits which produce an output voltage as a fraction of its input voltage
  • Has several resistors in series connected across a voltage source
  • Used to supply constant or variable potential difference from a power supply
  • Potential Dividers Study Mind

Using variable resistors

  • Potential divider supply a variable pd
  • Use variable resistor as one of the resistor in series
  • Vary the resistance across = vary pd output
  • Exported image

Using thermistor / LDR

  • Resistance decreases as temperature / light intensity increases
  • Used to trigger certain events
  • Mr Toogood Physics Potential dividers
  • FileThermistor potential dividersvg Wikimedia Comm...

Change in voltage across one resistor

  • Resistance stayed constant
    • Current increase / decrease \(\rightarrow\) voltage across changes
  • Resistance changed
    • The resistor has increased / decreased share of total resistance
    • New current is the same in both resistors
    • The resistor gets a larger / smaller share of the EMF

3.5.1.6 Electromotive force and internal resistance

Internal resistance of batteries

  • The resistance of the materials within the battery
  • Caused by electrons colliding with atoms inside the battery so some energy is lost before electrons leave the battery
  • Represented as a small resistor inside the battery

Terminal pd (\(V\))

  • Pd across the resistor(s)
  • \(V = \epsilon - Ir\)

Lost volts (\(v\))

  • Pd across the internal resistor in the battery
  • = energy wasted by the cell per coulomb of charge

Electromotive force

  • The energy converted (from chemical) to electrical energy by a cell for per coulomb of charge that passes through it
  • Can be measured by measuring the voltage across a cell using a voltmeter when there is no current running through the cell
  • \(\epsilon = \frac{E}{Q} = \frac{\text{electrical energy transferred}}{\text{charge}}\)
  • \(\epsilon = V + v = I(R + r) = \text{current} \times (\text{load resistance} + \text{internal resistance})\)

Required practical 6 - finding the EMF and internal resistance of a cell

Method

  • Set up the circuit as shown above with 2 (1.5V) cells connected in series
    • Exported image
  • Connect a voltmeter across the resistor to measure the load voltage
  • Close the switch so that the current flows in the circuit
  • Record the ammeter and voltmeter readings
  • Open the switch to cut off the current and prevent heating in the circuit
  • Replace the resistor with a different resistor with a different resistance and repeat the measuring process
  • Use at least 5 different resistors with different resistances
  • Repeat the experiment 2 more times for each resistor and calculate the mean current and voltage
  • Plot a graph of load voltage against current
  • EMF of the cell is the y-intercept of the graph while the internal resistance of the cell is the magnitude of the gradient of the graph

Safety

  • Another resistor can be included in series with the other to avoid high currents which could be dangerous and make the wires get hot

Improvements / controls

  • Only close the switch for as long as it takes to read off each pair of readings
    • Prevent the internal resistance of the battery or cell from changing during the experiment due to heating
  • Use fairly new batteries/cells
    • The emf and internal resistance of run down batteries can vary during the experiment