Electrical Resistance

Overview

• A lot of damage can be dealt if a short length of wire is connected to the positive and negative terminals of a cell/battery.
  • The wire and the source can get hot because a large current is flowing through them. Therefore, there is very little electrical resistance in the circuit, so the current is large.
• The current flowing in a circuit can be controlled by adding components with electrical resistance to the circuit.
• The greater the resistance, the smaller the current that will flow.

Defining resistance

• Resistance is a measure of how difficult it is for an electric current to flow through a device or a component in a circuit; it is the p.d. across a component divided by the current through it. $$ \text{resistance (\Omega)} = \frac{\text{p.d. (V)}}{\text{current (A)}} $$ $$R=\frac{V}{I}$$
• Ohms ($\Omega$) is the SI unit of electrical resistance. 1 $\Omega$ = 1 V/A

What is an ohm?

• In terms of the equation:
  • A p.d. of 10 V is needed to make a current of 1 A flow through a 10 $\Omega$ resistor.
  • A p.d. of 20 V is needed to make a current of 1 A flow through a 20 $\Omega$ resistor.
• Hence, resistance in ohms tells us how many volts are needed to make 1 A flow through that resistor. $$1\Omega =1\frac{V}{A}$$

Changing current

• The greater the resistance of a specific component, the harder it will be for the charge to flow, and so the current will be smaller.
• The greater the resistance in the circuit, the smaller the current that flows.
• The greater the p.d. in a circuit (or across a component), the greater the current that flows.

Resistance and thickness

• A long, thin wire has more resistance than a short, thick one.
• The longer a wire, the greater its resistance.
• The greater the diameter of a wire, the less its resistance.

Current-voltage characteristics

• A current-voltage characteristic is a graph of current on the vertical axis and voltage/p.d. on the horizontal axis.
  • The p.d. is the independent variable (the quantity that varies), therefore it is on the x-axis.
  • The current is the dependent variable (the quantity that varies as p.d. changes), therefore it is on the y-axis.
  • I-V characteristics can have both positive and negative voltages. This simply means that the power source is connected the other way around.
• An ohmic resistor is a resistor that has a constant resistance; its I-V characteristic is a straight line, so that the current through it is directly proportional to the voltage across it.

The filament lamp scenario

• In the current-voltage characteristic graph for a filament lamp, the graph is not a straight line through the origin, showing that the lamp is not an ohmic resistor.
  • Initially, while the voltage was low, the graph is straight, showing that the current increases at a steady rate as the voltage is increased.
  • At higher voltages, the graph starts to curve over. The current increases more and more slowly as the voltage is increased. Current is not proportional to voltage.
• There is a reason why the filament lamp is not an ohmic resistor:
  • At first, the voltage is low, therefore the current is small. The filament is relatively cool and the resistance is relatively low. A small increase in voltage produces a relatively large increase in current.
  • When increasing the voltage, the current also increases, but the filament gets hotter.
  • As the filament increasingly gets hotter, the resistance starts to increase.
    • The increase in current leads to an increase in the number of electrons flowing through the lamp and therefore the number of collisions between the electrons and the lattice increases.
    • Some of the kinetic energy from the electrons is transferred into internal energy, making the lattice vibrate more.
    • This increases the resistance because it increases the number of collisions between the electrons and the lattice. (Imagine moving through a crowd of people moving in random directions, and moving through a crowd of people standing still.)
  • As a result, the current does not increase as much for each additional increase in voltage. This causes the curve to become less steep.