Potential Dividers

Complete Electrical Circuits

What is a potential divider?

A circuit designed to provide a specific output voltage by splitting the supply voltage across two or more resistors.

How are resistors arranged in a simple potential divider circuit?

In series.

How is the supply voltage shared between resistors in a potential divider?

The voltage is split in proportion to the resistances.

Why is voltage divided between resistors connected in series?

The same current flows through each resistor and V = IR, so a larger resistance produces a larger potential difference.

What happens to the potential differences across resistors in series?

They add up to the total supply voltage.

What is the relationship between voltage and resistance in a two-resistor potential divider?

V₁/V₂ = R₁/R₂.

Write the potential divider equation for the output voltage across R₂.

Vout = Vin × R₂/(R₁ + R₂).

What does Vin represent in the potential divider equation?

The total input or supply voltage.

What does Vout represent in the potential divider equation?

The potential difference across the resistor from which the output is taken.

In Vout = Vin × R₂/(R₁ + R₂), what does R₂ represent?

The resistance across which the output voltage is measured.

Two resistors of 10 Ω and 20 Ω are connected across a 6 V supply. What is the total resistance?

30 Ω.

A 10 Ω and 20 Ω resistor are connected in series across 6 V. What current flows?

I = V/R = 6/30 = 0.20 A.

A 10 Ω and 20 Ω resistor form a potential divider across 6 V. What is the pd across the 10 Ω resistor?

V = IR = 0.20 × 10 = 2 V.

A 10 Ω and 20 Ω resistor form a potential divider across 6 V. What is the pd across the 20 Ω resistor?

V = IR = 0.20 × 20 = 4 V.

Why does the 20 Ω resistor receive twice the voltage of the 10 Ω resistor?

It has twice the resistance, so it receives twice the potential difference.

If one resistor has three times the resistance of another in a potential divider, how do their pds compare?

The larger resistor has three times the potential difference.

A 12 V supply is connected across R₁ = 100 Ω and R₂ = 500 Ω. Calculate Vout across R₂.

Vout = 12 × 500/(100 + 500) = 10 V.

What happens to Vout across R₂ if R₂ increases while R₁ remains constant?

Vout increases because R₂ receives a greater proportion of the supply voltage.

What happens to Vout across R₂ if R₂ decreases while R₁ remains constant?

Vout decreases because R₂ receives a smaller proportion of the supply voltage.

Why are potential dividers useful?

They allow a fixed supply voltage to provide a required smaller output voltage.

How can a potential divider produce an adjustable output voltage?

Use a variable resistor so that the resistance ratio, and therefore the output voltage, can be changed.

What happens when the resistance of a variable resistor in a potential divider is changed?

The proportion of the supply voltage across it changes.

How can a potential divider be used when investigating I–V characteristics?

A variable resistor can adjust the potential difference across the component being tested.

What is a potentiometer?

A potential divider made from a single resistance wire with a movable contact called a wiper.

What does the wiper of a potentiometer do?

It divides the resistance wire into two sections whose resistances depend on the wiper position.

Why does moving the wiper change the output voltage of a potentiometer?

It changes the relative resistances on either side of the wiper, changing how the supply voltage is divided.

What range of output voltages can an ideal potentiometer provide?

Any voltage from 0 V up to the full supply voltage.

How does the resistance of a uniform potentiometer wire depend on its length?

Resistance is directly proportional to length.

A 15 V supply is connected across a 40 cm potentiometer wire. What voltage corresponds to 10 cm of the wire?

15 × 10/40 = 3.75 V.

If the output of a potentiometer is measured from the 0 V end to a wiper 10 cm from the top of a 40 cm wire connected to 15 V, what is Vout?

The wiper is 30 cm from the 0 V end, so Vout = 15 × 30/40 = 11.25 V.

What is a sensor potential divider?

A potential divider in which one resistor is a sensor whose resistance changes with an environmental condition.

Give two sensor components commonly used in potential divider circuits.

A thermistor and an LDR.

What is an LDR?

A light-dependent resistor whose resistance changes with light intensity.

What happens to the resistance of an LDR as light intensity increases?

Its resistance decreases.

What happens to the resistance of an LDR as the surroundings become darker?

Its resistance increases.

How can an LDR potential divider be used to control a lamp?

The changing resistance of the LDR changes the output voltage, which can control the lamp.

If a lamp is connected in parallel with an LDR, what can be said about their voltages?

They have the same potential difference.

In the textbook sensor circuit, what happens to the LDR resistance when the surroundings become darker?

The LDR resistance increases.

In the textbook sensor circuit, what happens to the voltage across the LDR when it gets darker?

The voltage across the LDR increases.

In the textbook sensor circuit, what happens to the lamp as the surroundings become darker?

The lamp becomes brighter because the voltage across it increases.

In bright conditions, what happens to the resistance of the LDR?

It becomes very low.

Why is the lamp dim in bright conditions in the LDR circuit?

The low LDR resistance means only a small proportion of the supply voltage is across the LDR and therefore across the parallel lamp.

What happens to the voltage across the lamp as the LDR resistance increases?

It increases if the lamp is connected in parallel with the LDR.

How can a thermistor be used in a potential divider?

Its temperature-dependent resistance changes the output voltage as temperature changes.

For a standard NTC thermistor, what happens to resistance as temperature increases?

Resistance decreases.

How could a potential divider make a fan run faster as a kitchen becomes hotter?

Use a thermistor in the potential divider so its changing resistance causes the output voltage controlling the fan to increase as temperature rises.

What is meant by the switch-on voltage of an electronic component?

The minimum input voltage required for the component to switch on.

How can a sensor potential divider be used with a component that has a switch-on voltage?

The sensor resistance changes Vout until it reaches the switch-on voltage and activates the component.

How can the switching point of a sensor circuit be adjusted?

Change the value of the other resistor in the potential divider.

Why does changing the fixed resistor alter the switching point?

It changes the resistance ratio and therefore changes Vout for a given sensor resistance.

A potential divider has an 8 V supply, R₁ = 125 Ω and R₂ = 135 Ω. Calculate Vout across R₂.

Vout = 8 × 135/(125 + 135) ≈ 4.15 V.

What determines the fraction of Vin appearing across a resistor in a potential divider?

Its resistance as a fraction of the total series resistance.

If R₁ = R₂ in a two-resistor potential divider, what is Vout across either resistor?

Half of the supply voltage.

If R₂ is much larger than R₁, what happens to Vout measured across R₂?

Vout approaches the full supply voltage.

If R₂ is much smaller than R₁, what happens to Vout measured across R₂?

Vout approaches 0 V.

Why must you identify which resistor Vout is measured across before using the potential divider equation?

The numerator must contain the resistance across which Vout is measured.

How can you remember the potential divider equation?

Output voltage = input voltage × output resistance ÷ total resistance.