Electricity

• Current is the rate of flow of charge through a circuit, measured in amps (A)


  I = $\frac{Q}{t}$
• Electrical charge is measured in coulombs (C). One coulomb is the amount of charge that flows through a circuit in one second when the current is one ampere.
• To calculate the number of electrons passing a point, you divide the value for charge by e, $1.6 \times10^{-19}$
• Mean drift velocity is the average velocity attained by charged particles in a material due to an electric field. Charges move randomly but tend to drift in one direction.


  I = n A $e$ v
• Increasing the number of charged particles, increases current
• increasing the cross sectional area of the wire increases the current
• increasing mean drift velocity increases current
• In metals free electrons are the charge carriers, making them good conductors of electricity
• Conductors have high number densities, making them good electrical conductors
• Insulators have low number densities, making them bad electrical conductors
• Potential difference is the energy transferred from electrical energy to other forms per unit charge, measured in Volts (V)


  V = I R and V = $\frac{W}{Q}$
• When a charge is accelerated due to a potential difference, it gains kinetic energy. The work done on the charge is equal to the kinetic energy


  W = $e$ V = $\frac{1}{2}$ m v$^2$
• Power is the rate of doing work, measured in Watts (W).


  P = $\frac{W}{t}$ and P = I V
• Work done is power multiplied by time


  W = P t = V I t
• Electricity companies charge units of energy in kilowatt hours (kWh)


  E = P t
• Investigating resistance:

  1. Set up with a circuit using a variable power supply with a ammeter and voltmeter.
  2. Record the voltage and current values
  3. Change the voltage output and repeat the recordings
  4. Plot a graph of voltage against time
  5. The gradient of the line is the resistance
• Resistor I-V characteristics:

  Resistors are ohmic conductors and so have constant resistance when temperature is constant. The steeper the gradient, the lower the resistance

  
• Filament lamp I-V characteristics:

  Filament lamps are non-ohmic conductors.

  
• When a current flows through a filament, the temperature increases. As the temperature increases, the positive ions in the metal vibrate more vigorously which results in more collisions with electrons so it is harder for electrons to flow through the filament therefore the resistance of the filament increases.
• Diode I-V characteristics:

  When the voltage is negative, the resistance is extremely high and the current is almost negligible.

  When the voltage is above the threshold voltage, the resistance drops drastically and the current increases rapidly

  
• Resistance is effected by Length, Area and the resistivity of the material.
• As the length of a wire increases, the resistance increases.
• As the cross sectional area increases, the resistance decreases.
• Resistivity is the resistance encountered in a material that is 1 metre long and has a cross-sectional area of 1 square metre measured in ohm-metres (Ωm)


  R = $\frac{\rho L}{A}$
• Investigating resistivity:

  1. Measure the diameter of the wire using a micrometre and calculate its cross-sectional area
  2. Set up a simple circuit including a ohmmeter
  3. Record the resistance of the wire
  4. Vary the length of the wire and record new reading for resistance
  5. Plot a graph for length against resistance
  6. The gradient of the graph is $\frac{\rho}{A}$
  7. Multiply the gradient by the area to find the resistivity
• Kirchhoff's First law states that for any point in an electrical circuit, the sum of the currents into that point is equal to the sum of the currents out of that point, electrical charge is conserved.
• Kirchhoff's Second law states that in a closed loop of an electrical circuit, the sum of the e.m.f.s is equal to the sum of the p.d.s
• For series circuits, the current is the same throughout all parts of the circuit, the electromotive force is divided among the components and total resistance is the sum of the individual resistances.


  R$_{total}$ = R$_1$ + ... + R$_n$
• For parallel circuits, the total current is the sum of the currents in each branch, the potential difference is the same across all components and the total resistance is equal to one over the sum of one over the individual resistances.


  $\frac{1}{R_{total}}$ = $\frac{1}{R_1}$ + ... + $\frac{1}{R_n}$
• Electromotive force the energy transferred from chemical energy to electrical energy per unit charge, the work done on charge carriers per unit charge, measured in volts (V).
• The terminal potential difference is the energy per unit charge utilised in the external circuit and the potential difference across an electrical power source.
• Internal resistance leads to a loss of energy per unit charge known as lost volts


  E = IR + Ir = I(R + r)
• For cells in series, the total emf is the sum of the individual emf's
• For identical cells in parallel , the total emf is the equivalent to the emf of one of the cells.
• To investigate of emf into internal resistance

  1. Set up a circuit with a cell, variable resistor, switch and ammeter in series with a voltmeter in parallel to the cell
  2. Open the switch and record the emf of the cell from the voltmeter
  3. Close the switch and record the values of current and terminal p.d
  4. Vary the resistance of the variable resistor and record new values for current and p.d.
  5. Repeat the test to obtain more readings
  6. Plot a graph of current on the x against terminal p.d on the y
  7. the gradient is equal to -r
  8. and the y-intercept represents the emf of the cell
• A potential divider is a component which divides the source voltage

  V$_{out}$ = $\frac{R_2}{R_1 + R_2}$ V$_s$
• Thermistors are resistors with a negative temperature coefficients, so when temperature increases resistance decreases. This is because as the temperature of the semiconductor increases, some electrons gain enough kinetic energy and jump to the conducting band, increasing the number density of the material therefore the resistance of the material decreases
• Thermistors I-V Characteristics: As temperature increases, resistance decreases, and current increases

  
• The resistance of a light dependent resistor is inversely proportional to the light intensity. This is because when light intensity increases the number of charge carriers increases resulting in a decrease in resistance.
• A temperature sensor can be formed by placing the thermistor in series with a fixed resistor so as the temperature increases the resistance decreases which reduces the resistance overall increasing the current of the circuit which causes the voltage across the fixed resistor increases and the voltage across the thermistor to decrease