Potential Dividers

A potential divider is a simple circuit used to reduce a voltage to a lower level. It consists of two resistors connected in series. The voltage is divided between these resistors in proportion to their resistances.

The Potential Divider Equation

The voltage across each resistor in a potential divider can be calculated using the following equation:

$V_1 = \frac{R_1}{R_1 + R_2} \times V_{total}$

$V_2 = \frac{R_2}{R_1 + R_2} \times V_{total}$

Where:

• $V_1$ is the voltage across resistor R₁
• $V_2$ is the voltage across resistor R₂
• $R_1$ is the resistance of resistor 1
• $R_2$ is the resistance of resistor 2
• $V_{total}$ is the total voltage applied to the circuit

How the Potential Divider Works

When a voltage ($V_{total}$) is applied across the series combination of two resistors ($R_1$ and $R_2$), the current ($I$) flowing through both resistors is the same. The voltage drop across each resistor is proportional to its resistance. A larger resistance will experience a larger voltage drop.

Example Calculation

Consider a potential divider with $R_1 = 1000 \Omega$ and $R_2 = 2000 \Omega$ connected to a $12V$ supply.

1. Calculate the voltage across $R_1$ ($V_1$):

$V_1 = \frac{R_1}{R_1 + R_2} \times V_{total} = \frac{1000}{1000 + 2000} \times 12 = \frac{1000}{3000} \times 12 = 0.333 \times 12 = 4V$

2. Calculate the voltage across $R_2$ ($V_2$):

$V_2 = \frac{R_2}{R_1 + R_2} \times V_{total} = \frac{2000}{1000 + 2000} \times 12 = \frac{2000}{3000} \times 12 = 0.667 \times 12 = 8V$

As you can see, $V_1 + V_2 = 4V + 8V = 12V$, which is the total applied voltage.

Applications of Potential Dividers

Potential dividers are used in a variety of applications, including:

• Creating reference voltages for comparators.
• Adjusting the brightness of LEDs.
• Sensing changes in resistance.
• Voltage measurement (using a voltmeter).

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