Voltage Dividers - National 5 Recap
In a previous section, components in Series were discussed. For a Series circuit, the Voltage across each component added up to the supply Voltage. The diagram below shows a simple series circuit containing two Resistors:-
The values on the Voltmeters will add together to give the supply Voltage:-
Vs = V1 + V2
However, the value of each individual Voltage will depend on the Resistance of each Resistor, the larger the Resistance, the larger the Voltage share.
If the two Resistors have the same Resistance, then they will each have an equal share of the Voltage. In the above example, each Voltmeter would therefore show 6 V.
If the two Resistors had different Resistances, then they would share the Voltage following a ratio of their sizes:-
Where:-
Vs = Supply Voltage (V)
V1 = Voltage across Resistor 1 (V)
V2 = Voltage across Resistor 2 (V)
R1 = Resistance of Resistor 1 (Ω)
R2 = Resistance of Resistor 2 (Ω)
For the above circuit, what is the Voltages across each Resistor, if the Resistances of the Resistors are as follows:-
R1 = 10 Ω
R2 = 20 Ω
V1 = ( 10 / ( 10 + 20 ) ) x 12
V1 = ( 10 / 30 ) x 12
V1 = 4 V
Series circuit therefore:-
V2 = Vs - V1
V2 = 12 - 4
V2 = 8 V
Note - the Voltage divider formula could have been used a second time to calculate the value of V2, either method is valid.
Applications of Voltage Dividers
In the above circuit, two Voltmeters were attached across the Resistors, showing the Voltage across each. If instead of a Voltmeter, an additional circuit is attached across the Resistor, this Voltage share can be used. The circuit below shows an application of this:-
In the above diagram, two motors have been connected across the Resistors. As the right-hand Resistor has double the Voltage share of the left-hand Resistor, the motor on the right will rotate at twice the speed.
Wheatstone Bridges
The diagram below shows a Wheatstone Bridge circuit, which consists of two Voltage dividers working against each other:-
The reading on the Voltmeter between the two branches is the difference between the Voltages at the midpoint of each branch.
Example 2 -
The diagram below shows a Wheatstone Bridge circuit. Calculate the reading on the Voltmeter.
To find the Reading on the Voltmeter :-
1. Calculate V3 (the Voltage Across Resistor R3).
2. Calculate V4 (the Voltage across Resistor R4).
3. Calculate the Difference between the two.
Voltage across R3:-
Both Resistors are equal in value , therefore they will share the supply Voltage equally.
V3 = 12 / 2 = 6 V
Voltage across R4:-
The two Resistors have different values, therefore the ratio calculation above must be used:-
V4 = (R4/(R3 + R4 )) x Vs
V4 = (20/(10 + 20 )) x 12
V4 = 8 V
Reading on the Voltmeter:-
VMeter = V4 - V3
VMeter = 8 - 6
VMeter = 2 V
Balanced Wheatstone Bridges
In the below diagram, one of the fixed Resistors (R2) has been replaced with a variable Resistor:-
By varying the Resistance of Resistor R2 it is possible to set the Voltmeter to read zero. When the Voltmeter reads zero, the Wheatstone Bridge is said to be balanced.
For a balanced Wheatstone Bridge, the following formula applies:-
Note - In order for this equation to work, the correct Resistors must be placed in the correct way. The division is between Resistors on the same series branch. Treating the Voltmeter as an "Equals sign" also helps...
If a balanced Wheatstone Bridge has the Resistance of one of the Resistors changed, then the Voltmeter will show a reading. If this is plotted (up to 10% of the Total Resistor value) the following linear relationship can be found:-
Note - The above graph shows both a positive and negative Voltage range. This is important as these balanced Bridge circuits can be used not only to show small variations in Resistance, but also the direction of that change.
Applications of a Balanced Wheatstone Bridge
The following diagram shows a Wheatstone Bridge sensing circuit:-
In the above diagram there are four Resistors, two fixed Resistors, a variable Resistor and a Thermistor. The circuit above is designed to show small variations in temperature around a set value.
When at the required Temperature, the variable Resistor is adjusted so that the Wheatstone Bridge is balanced and therefore the reading on the Voltmeter is 0 V.
If the Temperature changes, the Bridge will move out of balance, proportionally with the Temperature change.
For the above set up :-
Temperature increases - The Voltmeter will show a positive Voltage
Temperature decreases - The Voltmeter will show a negative Voltage
This set up allows very small temperature changes to be measured, as well as the direction of these changes.
This Voltage could then be used as an input to a control system, such as central heating system, with the Wheatstone Bridge acting as the sensor in the Thermostat control.
