CIE A Level Physics復(fù)習(xí)筆記10.2.1 Potential Dividers
Potential Divider Circuit
- When two resistors are connected in series, through Kirchhoff’s Second Law, the potential difference across the power source is divided between them
- Potential dividers are circuits which produce an output voltage as a?fraction?of its input voltage
- Potential dividers have two main purposes:
- To provide a variable potential difference
- To enable a specific potential difference to be chosen
- To split the potential difference of a power source between two or more components
- Potential dividers are used widely in volume controls and sensory circuits using LDRs and thermistors
- Potential divider circuits are based on the ratio of voltage between components. This is equal to the ratio of the resistances of the resistors in the diagram below, giving the following equation:
Potential divider diagram and equation
- The input voltage Vin?is applied to the top and bottom of the series resistors
- The output voltage Vout?is measured from the centre to the bottom of resistor R2
- The potential difference?V?across each resistor depends upon its resistance?R:
- The resistor with the?largest resistance?will have a?greater potential difference?than the other one from?V?=?IR
- If the resistance of one of the resistors is increased, it will get a greater share of the potential difference, whilst the other resistor will get a smaller share
- In potential divider circuits, the p.d across a component is proportional to its resistance from?V?=?IR
Worked Example
The circuit is designed to light up a lamp when the input voltage exceed a preset value.
It does this by comparing Vout?with a fixed reference voltage of 5.3 V.
Vout?is equal to 5.3
Calculate the input voltage Vin.
Exam Tip
Always make sure the correct resistance is in the numerator of the potential divider equation. This will be the resistance of the component you want to find the output voltage of.
Variable Resistance Components
- Variable and sensory resistors are used in potential dividers to vary the output voltage
- This could cause an external component to switch on or off e.g. a heater switching off automatically when its surroundings are at room temperature
- Sensory resistors used are?Light Dependent Resistors (LDRs)?and?thermistors
LDR and thermistor in a potential divider circuit with a fixed resistor R
- The voltmeter in both circuits is measuring Vout
- Recall that the resistance of an LDR varies with light intensity
- The higher the light intensity, the lower the resistance and vice versa
- An LDR circuit is often used for street and security lights
- The resistance of a thermistor varies with temperature
- The hotter the thermistor, the lower the resistance and vice versa
- A thermistor circuit is used in fire alarms, ovens and digital thermometers
- From Ohm’s law?V = IR, the potential difference Vout?from a resistor in a potential divider circuit is?proportional?to its resistance
- If an LDR or thermistor's resistance?decreases, the potential difference through it also?decreases
- If an LDR or thermistor's resistance?increases, the potential difference through it also?increases
- Since the total p.d of the components must be equal to Vin, if the p.d of the sensory resistor?decreases?then the p.d of the other resistor in the circuit must?increase?and vice versa
Worked Example
A potential divider consists of a fixed resistor R and a thermistor.
What happens to the p.d through resistor R and the thermistor when the temperature of the thermistor decreases?
ANSWER:??D
- Due to Ohm’s Law (V = IR), both the resistor and thermistor are connected in series and have the same current I
- If resistance?R?increases, the potential difference across the thermistor also?increases
- In series, the potential difference is shared equally amongst the components. Their sum equals the e.m.f of the supply (Kirchhoff’s second law)
- If the potential difference across the thermistor?increases, the potential difference across the resistance R must?decreases, to keep the same overall total e.m.f
- This is row?D
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