Resistance (Cambridge International IGCSE Physics)

Ohm's law

Spec point — 4.2.9 · Recall and use the equation for resistance R = V/I Know that the p.d. across an electrical conductor increases as its resistance increases for a constant current

Ohm's law

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

• For a constant p.d., current and resistance are inversely proportional

  • If the resistance is doubled, current will halve

• This relationship is described by the equation for resistance

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

• Where:

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

Consequences of Ohm's law

• Resistors are used in circuits to control either:

  • the current in branches of the circuit (through certain components)
  • the potential difference across certain components

• This is due to the consequences of Ohm's law

  • The current in an electrical conductor decreases as its resistance increases (for a constant p.d.)
  • The p.d. across an electrical conductor increases as its resistance increases (for a constant current)

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

Determine the potential difference across the resistor.

[2]

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

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

$V=IR$ [1 mark]

Step 3: Substitute in the known values to calculate

$V=0.3\times12$

$V=3.6V$ [1 mark]

Current-voltage graphs

Spec point — 4.2.9 · Sketch and explain the current–voltage graphs for a resistor of constant resistance, a filament lamp and a diode

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

Linear I-V graphs are straight lines through the origin, indicating a constant resistance. Non-linear I-V 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)

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

  • filament lamps
  • diodes
  • LDRs
  • thermistors

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 I-V 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 wire or fixed resistor

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

I-V graph for a filament lamp

• The relationship between current and voltage for a filament lamp is non-linear, or not directly proportional, which means:

  • the I-V graph is not a straight line, so voltage and current do not increase (or decrease) by the same amount
  • the slope of the graph is not constant, so resistance changes

• The I-V graph for a filament lamp shows that as voltage increases:

  • the current increases at a proportionally **slower **rate
  • the resistance increases;**** the flatter the slope, the higher the resistance

As current flows through a filament lamp, the lamp heats up; resistance increases with temperature, causing the S-shaped curve

• As current through a filament lamp increases, the resistance increases because:

  • the higher current causes the temperature of the filament to increase
  • the higher temperature causes the atoms in the metal lattice of the filament to vibrate more
  • this causes an increase in resistance as it becomes more difficult for free electrons (the current) to pass through
  • since resistance opposes the current, this causes it to increase at a slower rate

I-V graph for a diode

• A diode allows current to flow in one direction only

  • This is called forward bias

• In the reverse direction, the diode has very high resistance, and therefore no current flows

  • This is called reverse bias

• When the current is in the direction of the arrowhead symbol, this is forward bias

  • On the I-V graph, this is shown by a sharp increase in voltage and current on the right side of the graph
  • This shows the resistance is very low

• When the diode is switched around, this is reverse bias

  • On the I-V graph, this is shown by a zero reading of current or voltage on the left side of the graph
  • This shows the resistance is very high

The current is zero at all potential differences in the negative quadrants because current only flows one way through a diode; this gives the diode I-V graph its distinct shape

Exam Hint In your IGCSE exam, you could be asked to recognise, sketch or explain the I-V graphs for a wire / fixed resistor (ohmic conductors), a filament lamp and a diode.