Variable Resistance (DP IB Physics): Revision Note
Variable Resistance
Thermistors
A thermistor is a non-ohmic conductor and sensory resistor whose resistance varies with temperature
Most thermistors are negative temperature coefficient (ntc) components.
This means that if the temperature increases, the resistance of the thermistor decreases (and vice versa)
The temperature-resistance graph for a thermistor is shown below
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Graph of temperature against resistance for a thermistor
Thermistors are temperature sensors and are used in circuits in ovens, fire alarms and digital thermometers
As the thermistor gets hotter, its resistance decreases
As the thermistor gets cooler, its resistance increases
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The resistance through a thermistor is dependent on the temperature of it
Light-dependent resistors (LDR)
A light-dependent resistor (LDR) is a non-ohmic conductor and sensory resistor
Its resistance automatically changes depending on the light energy falling onto it (illumination)
This is shown by the following graph:
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Graph of light intensity and resistance for an LDR
As the light intensity increases, the resistance of an LDR decreases
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Resistance of an LDR depends on the light intensity falling on it
LDRs can be used as light sensors, so, they are useful in circuits which automatically switch on lights when it gets dark, for example, street lighting and garden lights
In the dark, its resistance is very large (millions of ohms)
In bright light, its resistance is small (tens of ohms)
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LDRs are used for automatic street lights
Potentiometer
A potentiometer is similar to a variable resistor connected as a potential divider to give a continuously variable output voltage
It can be used as a means of comparing potential differences in different parts of the circuit
It is recognised on a circuit diagram with a resistor fitted with a sliding contact
The sliding contact has the effect of separating the potentiometer into two parts (an upper part and a lower part), both of which have different resistances
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Moving the slider (the arrow in the diagram) changes the resistance (and hence potential difference) of the upper and lower parts of the potentiometer
If the slider in the above diagram is moved upwards, the resistance of the lower part will increase and so the potential difference across it will also increase
Therefore, the variable resistor obtains a maximum or minimum value for the output voltage
If the resistance is 3 Ω:
Maximum voltage is when the resistance is 3 Ω
Minimum voltage is when the resistance is 0 Ω
Worked Example
A thermistor is connected in series with a resistor R and a battery.
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The resistance of the thermistor is equal to the resistance of R at room temperature. When the temperature of the thermistor decreases, which statement is correct?
A. The p.d across the thermistor increases
B. The current in R increases
C. The current through the thermistor decreases
D. The p.d across R increases
ANSWER: A
The resistance of the thermistor increases as the temperature decreases
Since the thermistor and resistor R are connected in series, the current I in both of them is the same
Ohm’s law states that V = IR
Since the resistance of the thermistor increases, and I is the same, the potential difference V across it increases
Therefore, statement A is correct
Worked Example
Which graph best represents the way in which the current I through an LDR depends upon the potential difference V across it?
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ANSWER: A
An LDR (Light Dependent Resistor) is a type of resistor whose resistance decreases as light intensity increases.
The relationship between current (I) and potential difference (V) across an LDR follows Ohm’s Law, but since resistance varies with light intensity, the shape of the I-V graph is nonlinear.
For a given light intensity, the LDR behaves as a non-ohmic conductor.
At low voltages, the current increases slowly because the resistance is high.
As V increases, the current increases more rapidly, indicating a decreasing resistance.
The shape is curved, rather than a straight line.
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