# 5.1.2 Current–Voltage Characteristics

### Ohm's Law

• Ohm’s law states:

For a conductor at a constant temperature, the current through it is proportional to the potential difference across it

• Constant temperature implies constant resistance
• Ohm’s law is represented in the equation below:

• The relation between potential difference across an electrical component (in this case, a fixed resistor) and the current can be investigated through a circuit such as the one below

Circuit for plotting graphs of current against voltage

• By adjusting the resistance on the variable resistor, the current and potential difference will vary in the circuit
• Measuring the variation of current with potential difference through the fixed resistor will produce a straight line graph, such as the one below

Circuit for plotting graphs of current against voltage

• Since the gradient is constant, the resistance R of the resistor can be calculated by using 1 ÷ gradient of the graph
• An electrical component obeys Ohm’s law if its graph of current against potential difference is a straight line through the origin
• A resistor does obey Ohm’s law
• A filament lamp does not obey Ohm’s law
• This applies to any metal wires, provided that the current isn’t large enough to increase their temperature

#### Worked Example

The current flowing through a component varies with the potential difference V across it as shown.

Which graph best represents how the resistance R varies with V?

#### Exam Tip

• In maths, the gradient is the slope of the graph
• The graphs below show a summary of how the slope of the graph represents the gradient

### I–V Characteristics

• As the potential difference (voltage) across a component is increased, the current also increases (by Ohm’s law)
• The precise relationship between voltage and current is different for different components and can be shown on an I-V graph
• For an ohmic conductor, the IV graph is a straight line through the origin
• For a semiconductor diode, the IV graph is a horizontal line that goes sharply upwards
• For a filament lamp, the IV graph has an ‘S’ shaped curve

I–V characteristics for an ohmic conductor (e.g. resistor), semiconductor diode and filament lamp

#### Ohmic Conductor

• The I–V graph for an ohmic conductor at constant temperature e.g. a resistor is very simple:
• The current is directly proportional to the potential difference
• This is demonstrated by the straight-line graph through the origin

#### Semiconductor Diode

• The I–V graph for a semiconductor diode is slightly different. A diode is used in a circuit to allow current to flow only in a specific direction:
• When the current is in the direction of the arrowhead symbol, this is forward bias. This is shown by the sharp increase in potential difference and current on the right side of the graph
• When the diode is switched around, it does not conduct and is called reverse bias. This is shown by a zero reading of current or potential difference on the left side of the graph

#### Filament Lamp

• The I–V graph for a filament lamp shows the current increasing at a proportionally slower rate than the potential difference
• This is because:
• As the current increases, the temperature of the filament in the lamp increases
• Since the filament is a metal, the higher temperature causes an increase in resistance
• Resistance opposes the current, causing the current to increase at a slower rate
• Where the graph is a straight line, the resistance is constant
• The resistance increases as the graph curves
• The filament lamp obeys Ohm’s Law for small voltages

#### Worked Example

The I–V characteristic of two electrical component X and Y are shown.

Which statement is correct?

A.     The resistance of X increases as the current increases
B.     At 2 V, the resistance of X is half the resistance of Y
C.     Y is a semiconductor diode and X is a resistor
D.     X is a resistor and Y is a filament lamp

• The I–V graph X is linear
• This means the graph has a constant gradient. I/V and the resistance is therefore also constant (since gradient = 1/R)
• This is the I–V graph for a conductor at constant temperature e.g. a resistor
• The I–V graph Y starts with zero gradient and then the gradient increases rapidly
• This means it has infinite resistance at the start which then decreases rapidly
• This is characteristic of a device that only has current in one direction e.g a semiconductor diode
• Therefore, the answer is C

#### Exam Tip

Make sure you’re confident in drawing the IV characteristics for different components, as you may be asked to sketch these from memory in exam questions

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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