Resistance (Cambridge International IGCSE Science)

Resistance

• Resistance is defined as: The opposition to current

• Resistance occurs because the free electrons flowing in the circuit (current) collide with the metal ions in the wire

• These collisions slow down the electrons, or, in other words, resist their flow

  • The higher the resistance of a circuit, the lower the current
  • This means that good conductors have a low resistance and insulators have a high resistance

• The resistance of a circuit can be increased by adding resistors (or variable resistors) to it

• Every electrical component has a resistance, even wires

  • In exam questions, the resistance of the wires and batteries are assumed to be negligible

The effect of resistance on the current in a circuit

When a circuit has a high resistance, a lower current will flow, and vice versa *

Ohm's law

• Current, $I$, potential difference, $V$, and resistance, $R$, all affect one another

• Changing any one of these in a circuit, changes all of them

• Current and resistance are inversely proportional

  • If the resistance is doubled, current will halve

• This relationship is described by the following equation, known as Ohm's law

$R=\frac{V}{I}$

• Where

  • $R$ = resistance, measured in ohms (Ω)
  • $V$ = potential difference, measured in volts (V)
  • $I$ = current, measured in amperes or amps (A)

Worked Example A 12 Ω resistor has a current of 0.3 A flowing through it.

Determine the potential difference across the resistor.

Answer:

Step 1: List the known quantities

• Resistance, $R=12Ω$
• Current, $I=0.3A$

Step 2: Write out the equation for Ohm's law and rearrange to make potential difference the subject

$R=\frac{V}{I}$

$V=IR$

Step 3: Substitute in the known values to calculate

$V=0.3\times12$

$V=3.6V$

Current-voltage graphs

Extended Tier Only

• The relationship between current and potential difference of a component can be shown on a current-voltage (I-V) graph

• When the relationship between current and potential difference is linear:

  • the I-V graph is a straight line which passes through the origin
  • the resistance is constant
  • these are known as ohmic resistors

• When the relationship between current and voltage is non-linear:

  • the I-V graph that is not a straight line
  • the resistance is not constant
  • these are known as non-ohmic resistors

Current-voltage (I-V) graph for a resistor and a filament lamp

Linear IV graphs are straight lines through the origin, indicating a constant resistance. Non-linear IV graphs are curved, indicating a variable resistance

• Components with linear I-V* graphs (ohmic resistors) include:

  • fixed resistors (at constant temperature)
  • wires (at constant temperature)

I-V graph for ohmic conductors

• The relationship between current and voltage for a wire or fixed resistor is linear, or directly proportional, which means

  • the IV graph is a straight line, so voltage and current increase (or decrease) by the same amount
  • the slope of the graph is constant, so resistance is constant

I-V graph for a a wire of fixed resistor

The current is directly proportional to the potential difference (voltage) as the graph is a straight line through the origin

Exam Hint In your IGCSE exam, you could be asked to recognise, sketch or explain the I-V graph for a wire or fixed resistor (ohmic conductors), but you do not need to know about the I-V graphs for a filament lamp or a diode.

Video of Resistance