5.2 Resistance

RESISTANCE IN CIRCUITS

LEARNING OBJECTIVES

  • 5.2.1: Explain how to determine the resistance of a wire or other component.
  • 5.2.2: Perform calculations using the relationship between resistance, voltage, and current.
  • 5.2.3: Explain the difference between ohmic and non-ohmic resistance.
  • 5.2.4: Describe how the resistance of an NTC (Negative Temperature Coefficient) or LDR (Light Dependent Resistor) depends on other variables.
  • 5.2.5: Explain how to set the desired resistance on an adjustable resistor.
  • 5.2.6: Use specific resistivity to calculate the resistance of a wire.

RESISTANCE DEPENDENCE ON APPLIANCES

  • Various household appliances operate at a standard 230 V mains voltage.
    • The current (I) varies significantly among these appliances.
    • Example: A tumble dryer draws more current than a light bulb, indicating different resistances.
  • Observation:
    • Higher current through an appliance generally indicates lower resistance to electron flow.

CALCULATING RESISTANCE

  • The resistance (R) of a circuit component can be calculated using:
    • Formula:
      R = rac{U}{I}
    • Where:
      • R = resistance in ohms (Ω)
      • U = voltage in volts (V)
      • I = current in amps (A)
  • The unit of resistance is named after Georg Simon Ohm (1789-1854).

EXAMPLE EXERCISE

  • Given: Light bulb specifications - 12 V and 50 mA.
    • Convert 50 mA to amperes: 50 mA = 0.050 A.
  • Calculation:
    R = rac{U}{I} = rac{12 ext{ V}}{0.050 ext{ A}} = 240 ext{ Ω} = 0.24 ext{ kΩ}

OHM'S LAW

  • The relationship between voltage (U) and current (I) for ohmic materials is direct proportionality.
  • Direct Relationships:
    • If voltage doubles, current doubles.
    • If voltage triples, current triples.
  • This consistency of resistance indicates an ohmic resistance.

RESISTANCE AND TEMPERATURE

  • Experiments with incandescent bulbs show that:
    • The resistance is not constant; it increases with temperature.
  • As voltage increases across a filament, it glows brighter, raising its temperature to about 2500 °C, which increases resistance.
  • Observation:
    • Most materials show increased resistance with temperature, except constantan wires, which have constant resistance even when heated. In many practical applications, temperature changes are negligible, allowing us to treat resistance as constant.

VARIABLE RESISTORS

  • Types of variable resistors:
    • NTC (Negative Temperature Coefficient) Resistor:
    • Sensitive to temperature changes.
    • As temperature increases, resistance decreases, allowing for better current conduction.
    • LDR (Light Dependent Resistor):
    • Sensitive to light levels.
    • Increased light exposure results in lower resistance and better current conduction.
  • Applications:
    • NTC as temperature sensors.
    • LDR as light sensors.

ADJUSTABLE RESISTORS

  • Variable Resistor:
    • Consists of a long, coiled wire.
    • A slider adjusts the length of wire included in the circuit, effectively changing the resistance value.
    • As the effective length of wire decreases, resistance decreases, allowing for custom resistance settings.

DIAGRAMS

  • Experiment Setups:
    • Figure 1: Setup for measuring voltage and current through a wire.
    • Figure 2: Circuit diagram for determining wire resistance.
    • Figure 3: (I,U) diagram for constantan wire, illustrating Ohm's Law with linear relationship.
    • Figure 4: (I,U) diagram for incandescent bulb, demonstrating non-ohmic behavior with increasing resistance.
    • Figure 5: NTC and its circuit symbol representation.
    • Figure 6: LDR and its circuit symbol representation.
    • Figure 7: Schematic of variable resistor, demonstrating usage in educational settings.