Understanding Output Voltage of Potential Divider Circuits
Learn how the output voltage of a potential divider circuit is affected, including the potential divider equation, examples, and the use of ratios to calculate output voltage.
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Potential Dividers AIM: To understand what affects the output voltage of a potential divider circuit (also known as a voltage divider) PRIOR KNOWLEDGE: Circuit rules for current and voltage, resistance and the resistor equation and how to use a voltmeter www.pfnicholls.com
Overview Potential dividers are a very common part of even the most complex circuits and it is therefore very important to understand what they do. A potential divider, also known as a voltage divider, is simply a pair of resistors in series There is an input voltage (Vin) and an output voltage (Vout) which is the voltage across R2 Examples include: A switch and pull down resistor used in logic circuits A thermistor and fixed resistor to make a temperature sensor
Overview what they do The potential difference across ONE of the resistors is a fraction of the applied EMF (Vin). The total potential difference across the resistors is divided between the two resistors, each having its own potential difference - hence potential divider. Apply a voltage to the input (Vin) and get a smaller voltage at the output (Vout) The output voltage is a fraction of the input voltage. The output voltage depends on (a) the input voltage Measure Vout with a voltmeter (b) the ratio of the two resistors.
The Potential Divider Equation The output voltage from a potential divider (Vout) is given by the potential divider equation: ??? ?2 ?1+?2 ????= It is important to be able to use this equation. The first 3 slides have all shown slightly different potential divider circuits but they are all the same circuit It is useful to be able to derive this equation
Example Vin = 9V R1 = 270 R2 = 560 Using the potential divider equation 9 560 270 + 560 ????= ????=5040 A voltmeter here would read 6.1 volts 830 ????= 6.1 ?
The Potential Divider Equation Rearranging the potential divider equation is non-trivial and, in most cases, unnecessary as other approaches can be used For reference, the potential divider equation rearranges to give: ???=???? ?1+ ?2 ?2 ??? ???? ?2 ???? ?1= ???? ?1 ??? ???? ?2=
Using Ratios The potential divider equation is very useful for calculating Vout but it is less obvious when trying to calculate R1 or R2. It is usually much easier to use the ratios of the voltages to work out what resistor values to use. The ratio of the voltages is equal to the ratio of the resistances: ?1 ?2 = ?1 ?2 OR ?1:?2 = ?1:?2 Knowing Vin and Vout means you know V1 and V2 (V2 = Vout) Once you know V1 and V2 you can choose R1 and R2 to be in the same ratio
Using Ratios Example 1. Calculate the voltage across each resistor V1 = 20 5 = 15V and V2 = 5V 2. Equate the ratio of the voltage and the ratio of the resistors 15:5 = R1:12k and 15:5 = 3:1 3. Calculate the value of the unknown resistor R1 = 3 x 12k = 36k
An important consideration The output voltage of a potential divider can only be calculated correctly if NO CURRENT flows from the output This applies when using the potential divider equation and when using ratios The current in R1 and R2 must be the same In the diagram, I1 = I2 If current flows from the output, use the circuit rules to calculate the various potential differences
Changing R1 Where one of the resistors in a potential divider is variable it is very important to know how Vout changes when either R1 or R2 changes (and Vin remains fixed). Case 1: R1 increases R1 increases and takes a larger share of the input voltage Therefore, the remaining voltage, Vout goes down R1 goes up Vout goes down
Changing R1 Case 2: R1 decreases R1 decreases and takes a smaller share of the input voltage Therefore, Vout goes up R1 goes down Vout goes up
Changing R2 Case 3: R2 increases R2 increases and takes a larger share of the input voltage Therefore, Vout goes up R2 goes up Vout goes up
Changing R2 Case 4: R2 decreases R2 decreases and takes a smaller share of the input voltage Therefore, Vout goes down R2 goes down Vout goes down
Using an LDR as R2 As the brightness increases the resistance of the LDR decreases As the resistance of the LDR decreases, Vout decreases Therefore, Vout goes down as the brightness increases As the brightness decreases the resistance of the LDR increases As the resistance of the LDR increases, Vout increases. Therefore, Vout goes up as it gets darker
Using an LDR as R1 As the brightness increases the resistance of the LDR decreases As the resistance of the LDR decreases, Vout increases. Therefore, Vout goes up as the brightness increases As the brightness decreases the resistance of the LDR increases As the resistance of the LDR increases, Vout decreases Therefore, Vout goes down as it gets darker
Summary A potential divider is two resistors in series The output voltage is a fraction of the input voltage A potential divider is also known as a voltage divider The output can be calculated using the potential divider equation: Vout = (Vin x R2) / (R1 + R2) The output voltage can be calculated using ratios because we know R1:R2 = V1:V2 where V2 is Vout No current flows from the output Increasing R1 makes Vout smaller and vice versa Increasing R2 makes Vout bigger and vice versa Vout depends on the ration of the resistor values, not the actual values
Questions 1. For Vin = 9V, R1 = 10k and R2 = 33k , what is Vout? 2. For Vin = 12V, R1 = 200 and R2 = 100 , what is Vout? 3. For Vin = 8V and R1 = 10k , what value of R2 gives Vout = 6V? 4. For Vin = 6V and R2 = 1k , what value of R1 gives Vout = 1.5V? 5. How does Vout change if Vin increases? 6. How does Vout change if R1 increases? 7. How does Vout change if R2 increases? 8. When can the potential divider equation NOT be used to calculate the output voltage?
Answers 1. Using the potential divider equation, Vout = (9 x 33)/43 = 6.9V 2. Using ratios, R1:R2 = 2:1 therefore Vout= x 12 = 4V 3. V2 = 6V gives V1 = 2V, V1:V2 = 1:3 therefore R2 = 30k 4. V2 = 1.5V gives V1 = 4.5V, V1:V2 = 3:1 therefore R1 = 3k 5. If Vin increases, Vout also increases 6. If R1 increases, Vout decreases 7. If R2 increases, Vout also increases 8. The equation cannot be used when current flows from the output and I1 I2
