Potential Divider

Overview

A potential divider is a circuit arrangement that uses resistors in series to divide an input voltage into smaller output voltages.

It is one of the most important DC-circuit ideas because it allows:

• adjustable output voltage
• sensor circuits
• reference voltages
• control systems

This topic supports DC Circuits.

Definition

A potential divider is a series-resistor arrangement that produces an output potential difference equal to a chosen fraction of the input voltage.

Why It Matters

Potential dividers are one of the main ways circuits convert:

• a fixed supply into a chosen output voltage
• a changing resistance into a measurable electrical signal
• temperature, light, or position changes into voltage changes

Key Representations

Divider Principle

For resistors connected in series:

• the same current flows through each resistor
• total potential difference equals the sum of voltage drops

$$V_{\text{in}}=V_1+V_2+\cdots$$

Since:

$$V=IR$$

a larger resistance gets a larger share of the voltage.

Two-Resistor Potential Divider

Two resistors $R_1$ and $R_2$ connected in series across input voltage $V_{\text{in}}$.

Total Resistance

$$R_{\text{total}}=R_1+R_2$$

Current

$$I=\frac{V_{\text{in}}}{R_1+R_2}$$

Voltage Across Each Resistor

$$V_1=I{R}_1=V_{\text{in}}\frac{R_1}{R_1+R_2}$$ $$V_2=I{R}_2=V_{\text{in}}\frac{R_2}{R_1+R_2}$$

Output Voltage Relation

If output is taken across $R_2$:

$$V_{\text{out}}=V_{\text{in}}\frac{R_2}{R_1+R_2}$$

This is the standard divider equation.

Ratio Form

For two series resistors:

$$V_1:V_2=R_1:R_2$$

Useful for fast mental checks.

Variable Divider

Replace one resistor with a variable resistor.

Changing resistance changes:

$$V_{\text{out}}$$

Common Uses

• volume controls
• brightness adjustment
• tuning knobs
• calibration controls

Sensor Applications

Potential dividers convert changing resistance into changing voltage.

Thermistor Divider

See also Thermistors and LDRs.

For a common NTC thermistor:

• temperature increases
• resistance decreases

Hence output voltage changes with temperature.

Uses

• thermostat circuits
• temperature alarms
• temperature sensing

LDR Divider

For an LDR:

• light intensity increases
• resistance decreases

Hence output voltage changes with light level.

Uses

• automatic street lighting
• camera light sensing
• security systems

Position Matters

Whether output rises or falls depends on where the sensor resistor is placed.

Example

If output is measured across lower resistor:

• lower resistance increases $\Rightarrow$ output increases
• lower resistance decreases $\Rightarrow$ output decreases

Always inspect circuit arrangement.

Loaded and Unloaded Divider

Unloaded Divider

No device draws current from output.

Standard divider formula applies directly.

Loaded Divider

Output connected to another component drawing current.

Then:

• effective resistance changes
• output voltage is usually lower than ideal

At H2 level, many questions assume unloaded divider unless stated otherwise.

Worked Example 1

Two resistors $2\Omega$ and $4\Omega$ connected across $12V$ supply.

Output taken across $4\Omega$ resistor.

$$V_{\text{out}}=12\frac{4}{2+4}$$ $$V_{\text{out}}=8.0V$$

Worked Example 2

A thermistor forms the lower resistor in a divider.

Temperature rises, thermistor resistance decreases.

Result

Output across thermistor:

$$V_{\text{out}}=V_{\text{in}}\frac{R}{R_{\text{top}}+R}$$

As $R$ decreases:

$$V_{\text{out}}\text{ decreases}$$

Common Exam Question Types

1. Calculate Output Voltage

Use divider formula directly.

2. Predict Direction of Change

Determine how resistance changes.

3. Design Sensor Circuit

Choose resistor positions so output increases or decreases as required.

4. Determine Unknown Resistance

Rearrange formula algebraically.

Common Mistakes

1. Using Parallel Formula

Potential dividers use series resistors.

2. Wrong Numerator

Use the resistor across which output is measured.

3. Assuming Equal Split

Voltage divides equally only if resistances are equal.

4. Ignoring Sensor Position

Top and bottom placement changes behaviour.

5. Forgetting Units

Use volts for output.

Quick Comparison Table

Situation	Output Across Lower Resistor
Lower resistance increases	increases
Lower resistance decreases	decreases
Upper resistance increases	decreases
Upper resistance decreases	increases

Links

• DC Circuits
• Current Electricity Fundamentals
• Potentiometer
• Circuit Fault Finding
• DC Circuits Common Exam Traps

Summary

A potential divider converts a fixed input voltage into a controlled output voltage.

Key ideas:

• same current in series
• voltage share proportional to resistance
• changing resistance changes output voltage
• useful for sensors and controls

Master this topic well because it appears frequently in H2 circuit questions.