Ohm's Law & I-V Characteristics
- 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:
- Measuring the variation of current with potential difference through a 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
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 eg. a fixed resistor:
- The I–V graph is a straight line through the origin
- For a non-ohmic conductor, such as
- A semiconductor diode, the I–V graph is a horizontal line that goes sharply upwards
- An LED (light-emitting diode), the I–V graph is similar to the semiconductor diode, since it is a specific diode that emits visible light
- A filament lamp, the I–V graph has an 'S' shaped curve
- A thermistor, the I–V graph is a curved line with increasing gradient through the origin
I–V characteristics for an ohmic conductor (e.g. resistor), semiconductor diode, filament lamp, LED and thermistor
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 which then goes steeply vertically down
- For an LED, the I–V graph is identical, except the sharp increase in p.d is further away from the origin as the frequency of the light increases
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
Thermistor
- The I–V graph for a thermistor is a shallow curve upwards
- The increase in the potential difference results in an increase in current which causes the temperature of the thermistor to rise
- As its temperature rises, its resistance decreases
- This means even more current is able to flow through
- Since the current is not directly proportional to the potential difference (the graph is still curved), the thermistor does not obey Ohm's Law
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
ANSWER: C
- 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
Examiner Tip
- Make sure you're confident in drawing the I–V characteristics for different components, as you may be asked to sketch these from memory in exam questions
Maths 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