Fixed resistors in series
Potential dividers divide up the voltage within a circuit, so that parts of a circuit only receive the voltage they require. Potential dividers usually consist of two or more resistors arranged in series across a power supply.
Fixed resistor in series with an LDR
Potential dividers form an important part of sensor circuits. For example, an LDR [LDR: A Light Dependent Resistor, or LDR, is a type of resistor which is affected by changes in light levels. A cadmium sulphide layer causes a decrease in resistance in the light and increase in the dark. ] or thermistorthermistor: An electrical device whose resistance decreases as its temperature increases. can be used in place of one of the resistors, with the output voltage signal being directed to an op-amp [operational amplifier: A device which takes a relatively weak signal as an input and produces a much stronger signal as an output. ] or IC.
Variable resistor in series with a thermistor
Instead of using a fixed resistor, a variable resistor allows the output voltage to be adjusted. A low-value fixed resistor should be placed in series with the variable resistor to prevent the full power of the circuit from being routed down the output voltage path if the variable resistor is accidentally moved to a low resistance.
Common uses of potential dividers
Potential dividers are important in both transistor-switching circuits and op-amp comparator circuits [Comparator circuits: Circuit with a comparator - a component which compares two voltages and gives either a high or low output depending on the result of the comparison. ]. The diagram shows a darkness-sensor circuit with a transistor [transistor: Components which do not conduct electricity unless they are turned on by a (different) electrical current. This means they can be used as switches, amplifiers and in other ways. ] used as a switch. When the LDR senses a drop in light, the LED is switched on.
- When the LDR has light falling on it, its resistance is low, usually around 400 ohms.
- When the LDR is covered up, the resistance increases (often to many kilo-ohms).
When the resistance of the LDR is small, its share of the voltage supply is small too; this means that the output voltage (Vout) from the voltage divider is small and the transistor is switched off.
In the dark the large resistance of the LDR takes a large share of the voltage supply so Vout is large and the transistor and LED both switch on.
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A potential divider, or potentiometer, consists of a number of resistors, and a voltmeter. The voltage read by the voltmeter is determined by the ratio of the resistances on either side of the point at which one end of the voltmeter is connected.
To understand how a potential divider works, let us consider resistors in series. The resistances add up, so, in a circuit with two resistors:
If we apply Ohm's law, remembering that the current is constant throughout a series circuit:
Multiply by current (I):
So, just as the resistances in series add up to the total resistance, the potential differences add up to the total potential difference. The ratios between the resistances are equal to the ratios between the potential differences. In other words, we can calculate the potential difference across a resistor using the formula:
In many cases, you will be told to assume that the internal resistance of the power source is negligible, meaning that you can take the total potential difference as the EMF of the power source.
A potential divider may work by combining a variable resistor such as an LDR or thermistor with a constant resistor, as in the diagram below. As the resistance of the variable resistor changes, the ratio between the resistances changes, so the potential difference across any given resistor changes.
Alternatively, a potential divider may be made of many resistors. A 'wiper' may move across them, varying the number of resistors on either side of the wiper as it moves, as in the following diagram:
1. A 12 kΩ resistor and a 20 kΩ resistor are connected to a 9V battery. A voltmeter is connected across the 12kΩ resistor. What is the reading on the voltmeter? (Assume negligible internal resistance.)
2. A potential divider consists of 100 5Ω resistors, with a wiper which moves on one resistor for every 3.6° a handle connected to it turns. The wiper is connected to a voltmeter, and the circuit is powered by a 120V power source with negligible internal resistance. What is the reading on the voltmeter when the handle turns 120°?
3. A 9V battery with internal resistance 0.8Ω is connected to 3 resistors with conductances of 3, 2 and 1 Siemens. A voltmeter is connected across the 3 and 2 Siemens resistors. An ammeter is placed in the circuit, between the battery and the first terminal of the voltmeter, and reads 2A. What is the reading on the voltmeter?