Electrical circuits

• Internal resistance and lost volts:

  • A source of emf has some internal resistance
  • Not all energy transferred to the charge carriers is available to the circuit, as some is transferred to the internal resistance of the cell
  • This results in a difference between the measured pd across the terminals of the power supply & the actual emf of the cell, which is referred to as the lost volts & is equal to the pd across the internal resistor
• • The internal resistance can be modelled as the source of emf being in series with its internal resistance, r. For a circuit with this power source attached to a resistor of resistance R, we can us the equation:
  • E = I(R+r)
  • to model the circuit. IR is equal to the V, the terminal pd of the cell, & Ir is equal to the lost volts
• Potential dividers:

  • V out = (R2/ R1+R2) x V in
  • where V in is the emf of the circuit, and V out is the p.d across R2
  • Potential divider circuits are set up with a p.d distributed across 2 resistors, with one of the resistors being connected to another circuit which uses the V out pd.
  • One of the resistors is typically a sensor or variable resistor, so that the resistance of the V out resistor is decreasing in proportion to the total circuit resistance, the pd across this resistor, V out will also decrease
• Ohm's law --> For conductors at a constant temperature the current is directly proportional to the pd across it.
• Ohmic/ normal metal --> Applies to any metal wires provided that the current isn't large enough to increase their temperature
• • Resistance is caused by collisions between electrons and positive ions
  • resistivity = a property of a material
  • resistance = property of an object
  • resistance is directly proportional to length
  • increasing the cross sectional area increases the routes available to charges and so decreases resistance.
  • Doubling the area halves the resistance
  • resistance is inversely proportional area
• Resistance = (resistivity x length) / area
• Resistivity = (resistance x area) / length
• • Resistivity of a material varies with temperature
  • for metals when temperature is increasing, fixed metal ions will vibrate at a greater frequency and amplitude. This increases the number of collisions of electrons with the ions, increasing the resistance
  • for semiconductors, the number density of charge carriers increases with increasing temperature, so the resistance of the material decreases
• • Some semiconductors have a negative temperature coefficient (NTC).
  • As the temperature of the material increases, the resistance of the material decreases
  • Change in resistance is dramatic therefore useful in temperature sensing circuits. E.g: thermistors & thermostats
• • Thermistors are non-ohmic components which is used to electrically measure the temperature
  • Made of an NTC semiconductor material, & as the current * temperature through the thermistor increases, the resistance decreases
• • Light dependent resistors (LDRs) are small, non-ohmic components made from semiconductors
  • When light intensity incident on the resistor is increasing, the resistance of the LDR decreases
  • I is inversely proportional to d^2