Advanced circuit behaviour (Topic 3B)
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A potential divider circuit is used to vary the potential difference (p.d.) output , connected to a fixed potential difference input A simple potential divider circuit consists of two resistors in series.
A potential divider is used to supply an external circuit with any p.d. between zero and the p.d supplied by the power source,
Kirchhoff’s second law states that the total p.d. supplied by the power source equals the sum of the p.d. across each resistor.
The resistances of the resistors determine the p.d. output. The resistor with the larger share of the total resistance receives a greater share of the total p.d.
A potential divider is used to split the potential difference of a power supply, but in some applications, the output voltage needs to vary.
The output voltage of a potential divider can be varied by replacing one of the fixed resistors with a variable resistor. As the resistance of the variable resistor changes, so does its share of the input p.d. causing to change in response.
Thermistors can be used as one of the resistors in a potential divider circuit, in order to provide a that varies with temperature input. This circuit could form part of a temperature sensor.
The resistance of a thermistor varies with its temperature:
- The higher the temperature of a thermistor, the lower its resistance.
- A higher temperature excites charge carriers in the thermistor, reducing the resistance.
When the temperature increases, the thermistor’s resistance drops. This results in the thermistor receiving a smaller fraction of the input voltage leading to a decrease in the output voltage Conversely, will rise when the temperature decreases.
A light-dependent resistor (LDR) can also be used as part of a potential divider circuit to provide an output voltage that varies in proportion to the intensity of the light. For example, an LDR could form part of a light sensor.
The resistance of a light-dependent resistor (LDR) varies with the light intensity incident on it:
- The higher the light intensity incident on an LDR, the lower its resistance.
- Incident light (of a sufficiently high frequency) excites charge carriers in an LDR, thereby reducing the resistance.
When light intensity is high, the LDR’s resistance is low. Consequently, it receives a smaller fraction of the input voltage resulting in a decrease in the output voltage Conversely, when the light intensity is low, the output voltage will increase.
Circuits with a low that require a varying may use a potentiometer instead of two separate fixed resistors. A potentiometer consists of three terminals and a sliding contact.
The position of the contact determines how the p.d. is shared between the two terminals and therefore the value of
As the slider is moved down, becomes smaller and becomes larger. now has a smaller share of the overall resistance and receives a smaller share of the overall voltage, resulting in a decrease in The inverse will happen if the slider is moved up.
An example of this type of circuit would be a sound volume control. Adjusting the sliding contact on the volume control changes the share of resistance and, therefore, the voltage output. The output would be connected to a speaker whose volume would change in response to the voltage level.
The voltage out for a potential divider circuit can be found using:
Where:
- is the resistance of resistor 1 measured in ohms.
- is the resistance of resistor 2 measured in ohms and this is the resistor where is measured.
- is the voltage across both resistors supplied by a power supply, measured in volts.
The potential divider equation is derived starting with Kirchhoff’s first law. For a potential divider circuit with fixed resistors and Kirchhoff’s first law states that the current is the same through both resistors.
Using Ohm’s law, the p.d. across resistor and (R_2\) respectively is:
These expressions show that the ratio of to is the ratio of the resistances:
is equal to the sum of the p.d. across each resistor, while is equal to the p.d. across resistor
The ratio of to is therefore:
The electromotive force (EMF) of a power source is the amount of energy converted to electrical energy per unit charge.
EMF is similar to potential difference but is used when work is done on the charge carriers, such as by a power source like a cell or battery.
Examples of this include:
- Common batteries used in electrical circuits convert chemical energy into electrical energy.
- Solar cells, which convert light energy into electrical energy, and thermocouples which convert thermal energy into electrical energy.
EMF in is given by the formula:
Where:
- is the work done in on the charges by the power source
- is the charge in passing through the power source.
It is important to note that EMF is not a force and is measured in volts the same as potential difference.
Moreover, the word ‘force’ in electromotive force originates from the way a power source transfers energy to the charges moving through it, which drives them around a circuit.
EMF and potential difference are both measured in and are both defined as the energy transferred per unit charge. However, they both have a discrete key distinction:
- EMF is used when work is done on the charge carriers, and the charge carriers gain energy.
- Potential difference is used when work is done by the charge carriers, and the charge carriers lose energy.
An example of this is illustrated in the diagram above.
- Work is done on charge carriers as they move through a battery and are given energy.
- However, work is done by the charge carriers when they move through a filament bulb; the electrical energy of the charge carriers is converted into thermal energy and light energy.
The electromotive force (EMF) of a source in a circuit, such as a cell or battery, is the energy per unit charge transferred from chemical energy to electrical energy.
Internal resistance Real cells and batteries have some resistance to the flow of current within themselves. This resistance causes energy to be lost as heat inside the source.
Generally, the voltage across the terminals of a cell or battery is less than its EMF as some energy is lost due to internal resistance.
A real cell of EMF, and internal resistance, can be modelled as an ideal cell (defined as a cell with no internal resistance) of EMF, in series with a fixed resistor of resistance
The electromotive force, (EMF) of a source in a circuit such as a cell or battery is energy per unit charge transferred from chemical energy to electrical energy. Note that some of this electrical energy will be dissipated as heat across the internal resistance.
The terminal potential difference, of a cell or battery is the energy per unit charge transferred to electrical energy in the external circuit. The terminal potential difference of a cell or battery can be measured by connecting a voltmeter across its terminals.
‘Lost volts’ refers to the energy per unit charge wasted as heat inside a battery or cell. It is the drop in potential across the battery or cell’s internal resistance.
Due to Kirchhoff’s second law (conservation of energy), we have:
It is important to recall the potential difference across the terminals of a battery or cell.
Question walkthrough
Explaining Why Terminal Voltage Is Less Than EMF
Explain why the terminal voltage of a cell in series with a resistor is less than its EMF, in terms of internal resistance and energy loss.
Lost volts, due to internal resistance inside a source of EMF is given by:
Where:
- is the current flowing through the source of EMF, and
- is its internal resistance.
Terminal potential difference, of a source of EMF is given by:
Where:
- is the current flowing through the source of EMF, and
- is the total resistance of the external circuit.
The EMF of a source is given by:
which may be written as:
To determine internal resistance and EMF of a power source:
- Set up a circuit with a variable resistor connected in series with the power source.
- Vary the resistance of the variable resistor and record voltage and current.
- Plot a graph of against
- The equation, tells us that the Y intercept gives the EMF and the gradient of the line gives the negative internal resistance
Question walkthrough
Calculating Lost Volts and Internal Resistance of a Battery
Calculate the lost volts and internal resistance of a battery in series with a resistor, given the EMF and circuit current.
Question walkthrough
Finding Internal Resistance from Voltmeter Percentage Drop
Determine the internal resistance of a cell in terms of the external resistance, given the percentage decrease in voltmeter reading when a switch is closed.
Question walkthrough
Finding EMF in Two Opposing Cells Circuit
Calculate the EMF of a cell using two cells with opposing EMFs and internal resistance connected to an external resistor, applying Kirchhoff's voltage law to a single-loop circuit.
The resistivity of a metal increases with temperature. When the temperature of a wire increases, the positive metal ions gain thermal energy and vibrate with a greater amplitude around their mean positions.
- Larger vibrations of the metal ions in a current-carrying wire result in more collisions between the electrons and the metal ions.
- A greater number of collisions leads to the electrons losing more energy as they move through the wire, causing them to move through the wire more slowly.
- Slower-moving electrons result in a lower current for a given potential difference and therefore a larger resistance.
In some semiconductors, an increase in temperature results in a decrease in resistance, unlike in metals. These semiconductors exhibit a negative temperature coefficient (NTC).
In NTC semiconductors, an increase in temperature leads to an increase in number density which is the number of charge carriers per unit volume.
A larger number density leads to an increase in current for a given potential difference, and hence a decrease in resistance.
Question walkthrough
Resistivity
Sketch how resistivity varies with temperature for an intrinsic semiconductor, linking the shape of the graph to how charge carrier number density changes with temperature.
A thermistor is an electrical component made from a negative temperature coefficient (NTC) semiconductor. The thermistor circuit symbol is a fixed resistor with a line through it.
A thermistor is a variable resistor because its resistance, and hence resistivity, decreases with temperature.
It is useful to note that thermistors are used in temperature-sensing circuits. Thermistors are used to monitor the temperature of complex electrical devices, such as computers and mobile phones, as well as household appliances like kettles and toasters.
The decrease in resistance of a thermistor with temperature is not linear.
Initially, the drop in resistance is quite steep, indicating a high sensitivity to small temperature changes. As the temperature continues to increase, the rate at which the resistance decreases becomes more gradual.
The resistance–temperature relationship for a thermistor can be determined using the experimental setup below.
- A waterproof thermistor is submerged in a hot water bath. The thermistor is connected to an ohmmeter to measure its resistance as the water cools.
- By taking readings of temperature and resistance using the thermometer and ohmmeter at set time intervals, respectively, you can observe the relationship between resistance and temperature of a thermistor experimentally.
Alternatively, if an ohmmeter is not available, the thermistor can be connected across a battery in series with an ammeter to measure the current, through it, and in parallel with a voltmeter to measure the potential difference, across it. The thermistor resistance can then be calculated from Ohm’s law:
The currents and voltages must be low to ensure the thermistor obeys Ohm’s law.
A light-dependent resistor (LDR) is a non-ohmic conductor.
The resistance of an LDR is inversely proportional to the amount of incident light.
An LDR is made of a material such that when light shines on it, more charge carriers are made available to carry current, decreasing the resistance.
LDRs have applications in light-sensing circuits. For example, LDRs are used in street lights, which only turn on when the background light level is low.
Question walkthrough
Explaining Meter Readings in an LDR Circuit
Explain how ammeter and voltmeter readings change in a series LDR circuit as light intensity and a variable resistor's resistance are altered.