Understanding Voltage Dividers

A voltage divider is a simple circuit that converts a higher voltage into a lower one using two resistors in series. The output voltage is a fraction of the input voltage, determined by the ratio of the two resistors.

The formula for the output voltage in a voltage divider is:

\[ V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2} \]

Where:

• \(V_{in}\) is the input voltage (V)
• \(V_{out}\) is the output voltage (V)
• \(R_1\) is the resistance of the first resistor (Ω)
• \(R_2\) is the resistance of the second resistor (Ω)

Example Calculations

Example 1:

If \(V_{in} = 12V\), \(R_1 = 10kΩ\), and \(R_2 = 5kΩ\):
\[V_{out} = 12 \times \frac{5000}{10000 + 5000} = 4V\]

Example 2:

If \(V_{in} = 9V\), \(R_1 = 2kΩ\), and \(R_2 = 1kΩ\):
\[V_{out} = 9 \times \frac{1000}{2000 + 1000} = 3V\]