Describe the action of a variable potential divider

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IGCSE Physics - 4.3.3 Variable Potential Divider

Variable Potential Divider

Description

A variable potential divider is a circuit that allows a user to select a fraction of the input voltage. It typically consists of two resistors connected in series. The voltage at the point between the two resistors can be adjusted by changing the value of one of the resistors.

Circuit Diagram

Suggested diagram: A circuit showing a voltage source (V), two resistors (R1 and R2), and a voltmeter connected across R2 to measure the output voltage (Vout).
Symbol Component
Resistor (R)
Voltage Source (V)
Voltmeter

Working Principle

When resistors are connected in series, the current through them is the same. The voltage drop across each resistor is proportional to its resistance. The potential divider works by creating a voltage drop across one of the resistors (R2), which is a fraction of the total input voltage (V). The ratio of the resistors determines the fraction of the voltage.

Formula

The voltage at the output (Vout) of a potential divider is calculated using the following formula:

$$V_{out} = V \times \frac{R_2}{R_1 + R_2}$$

Where:

  • Vout is the output voltage.
  • V is the input voltage.
  • R1 is the resistance of the first resistor.
  • R2 is the resistance of the second resistor.

How it Works (Step-by-Step Explanation)

  1. A voltage source (V) is connected across the series combination of two resistors (R1 and R2).
  2. Current flows through both resistors because they are in series. The current (I) is the same through both.
  3. The voltage drop across each resistor is given by Ohm's Law: V = IR. Therefore, the voltage drop across R1 is V1 = IR1 and the voltage drop across R2 is V2 = IR2.
  4. The total voltage (V) is the sum of the voltage drops across the two resistors: V = V1 + V2.
  5. Substituting the voltage drops from Ohm's Law, we get V = IR1 + IR2.
  6. Rearranging the equation to solve for V2 (the voltage at the output, which is across R2), we get V2 = V - IR1.
  7. Substituting I = V/R1, we get V2 = V - (V/R1) * R1 = V - V = 0. This is incorrect.
  8. Let's use the formula directly: Vout = V * (R2 / (R1 + R2)). This shows that Vout is a fraction of V, determined by the ratio of R2 to the total resistance (R1 + R2).

Applications

  • Volume control: In audio equipment, a potential divider is used to adjust the volume by varying the resistance of one of the resistors.
  • Brightness control: In lighting circuits, a potential divider can be used to control the brightness of a light by adjusting the amount of current flowing through the lamp.
  • Calibration circuits: Potential dividers are used to create precise voltage references for calibration purposes.
  • Potentiometers: A potentiometer is a type of variable resistor that uses a sliding contact to vary the effective resistance of a potential divider.