5.1 current electricity

• Charge - carried by electrons and positrons

  • Equal and opposite charge

  Current - the rate of flow of charge

  • Current is conserved
  • Assume a positive charge travels from + to - 
  • Electron flow is a negative charge travelling - to + 

  I = Q/t  current = change in charge / change in time
• Potential difference (voltage) - the work done (energy transferred) per unit charge (coulomb)

  • Electrons ‘do work’ as they pass through components in a circuit 
  • Electrons transfer energy
  • The difference in energy before and after the component is the energy transferred

  V = W/Q  voltage = work done (J) / unit charge (C)

  Resistance - the ratio of potential difference across a component to the current

  R = V/I  V = IR
• Ohm’s law

  For fixed resistance, the potential difference is proportional to the current

  V∝I     V=kI

  Ideal resistance

  • Ideal ammeters have 0 resistance 
  • Ideal voltmeters have infinite resistance
• I-V graphs 

  • Resistance is the ratio of the p.d. across a component to the current running through it
  • A resistor’s I-V graph is proportional and linear
  • A filament lamp’s I-V graph is a changing proportionality - inversely proportional becomes linear
  • I or V can be on the horizontal axis

  Ohmic vs. non-ohmic

  • An ohmic conductor obeys Ohm’s law
  • Ohmic - linear
  • Non-ohmic - non-linear

  
• Resistivity is specific to a material 

  • Measured in ohms

  = RA / L   resistivity = (resistance x area) / length
• Core practical (5)

  Determination of resistivity of a wire using a micrometre, ammeter and voltmeter

  • Measure the diameter of the wire using a micrometre.
  • The measurement should be taken between 5-10 times randomly along the wire.
  • Calculate the mean diameter from these values
  • Set up the equipment so the wire is taped or clamped to the ruler with one end of the circuit attached to the wire where the ruler reads 0.
  • The ammeter is connected in series and the voltmeter is in parallel with the wire

  
• • Attach the flying lead to the test wire at 0.25 m and set the power supply at a voltage of 6.0 V.
  • Check that this is the voltage across the wire on the voltmeter
  • Read and record the current from the ammeter, then switch off the current immediately after the reading
  • This is to prevent the wire from heating up and changing the resistivity
• • Vary the distance between the fixed end of the wire and the flying lead in 0.25 m intervals (0.25 m, 0.50 m, 0.75 etc.) until the full length
  • In this example, a 2.0 m wire is used.
  • The original length and the intervals can be changed (e.g. start at 0.1 m and increase in 0.1 m intervals), as long as there are 8-10 readings
  • Record the current for each length at least 3 times and calculate an average current, I
  • For each length, calculate the average resistance of the length of the wire using the equation
• Resistors

  • The current takes the path of least resistance
  • Resistors in series add together to equal the total resistance 

  Rt=R1+R2

  • Resistors in parallel result in a total resistance less than the smallest resistance

  1Rt=1R1+1R2

  • Current has more routes to go through - less total resistance

  
• Kirchoff’s laws

  Law 1

  • The sum of the currents leaving any junction is always equal to the sum of the currents that enter it

  Law 2

  • The total voltage across a circuit loop is equal to the sum of the voltage drops across the components in the loop
  •  The sum of any emfs in a closed loop = sum of any pd in a closed loop
  • In series circuits, the voltage will change across components
  • In parallel circuits, voltage through each parallel loop is the same as the emf
• Electricity relationships

  • Energy and Power

  E = IVt

  $P =$$IV =$$I^2R =$$V^2/R$

  • The relationship between the current and voltage is directly proportional
• Potential difference equations

  V1 = R1 / Rt   voltage = resistance / total resistance

  I = Vin / Rt   current = voltage in / total resistance

  $V_1=$$IR_1=$$(V_inR_1)/R_t$

  Emfs with multiple resistors

  • To supply a fixed pd when a source when a source pd is higher than needed
  • To supply a variable pd that you can control using a variable resistor
  • To supply a variable pd depending on external conditions
• Potentiometers

  • 0-100
  • Have a large range
  • Can have 0v
  • Can slide along resistor coil to give any resistance within the range
  • Advantage - large range
  • Disadvantage - wastes power

  Rheostats

  • Maximum 100v
  • Cannot reach 0v minimum
  • Can be any point along the coils
  • Resistance changes - more coils to travel through
  • Advantage - doesn't waste power; easier to connect
  • Disadvantage - never reaches 0v

  
• Emf - electromotive force

  • (emf value)J of work done in moving 1C of charge through the cell
  • = V + IR     emf = terminal p.d. + lost volts
  • =IR + Ir     emf=total current(total external resistance +internal resistance)

  IR - internal resistance

  • All cells have an internal resistance, r
  • The charge does work as it moves through the battery 
  • work done = lost volts
• Core practical - investigating EMF and internal resistance

  Aims

  • Investigate relationship between emf and internal resistance
  • Measuring variation of current and voltage using variable resistor

  Test variables

  • Independent variable - resistance, R
  • Dependent variable - voltage, V; current, I
  • Control variable - emf of a cell, the internal resistance of a cell
• Equipment

  • 1.5V cell - provide emf to circuit
  • Resistor - unknown resistance, to act as internal resistance
  • 100 variable resistor - change values of current and voltage in a circuit
  • Voltmeter - 0-2V range, to measure voltage
  • Resolution - 1mV
  • Ammeter - 0-200mA range, to measure current
  • Resolution - 0.1mA
  • Wires - 6+ leads, to make electrical connections
  • Switch - to open between readings so the battery isn't run down
• Method

  1. Connect the cell and resistor in series to be considered a single-cell
  2. Open the switch, and record the reading V on the voltmeter
  3. Set variable resistor to the maximum value, close switch and record voltage and current - keep the switch open between readings
  4. Vary the resistance of the variable resistor to a minimum of 8-10 readings, recording voltage and current for each resistance - take readings for whole range of variable resistor

  
• Current

  • series - same through all components
  • parallel - distributed in ratio through components

  Voltage

  • series - distributed in ratio across components
  • parallel - same across all components

  Voltage is the cause, current is the effect