Understanding Voltage Drops in Series and Parallel Resistors: A Practical Example

When working with electrical circuits, understanding the voltage drop across resistors is crucial for assessing overall circuit performance and ensuring safe operation. This article will delve into how to calculate the voltage drops for resistors arranged in both series and parallel, using a specific example of a 12V, 6Ω resistor in series with two 10Ω resistors in parallel.

Step 1: Calculate the Equivalent Resistance

In a circuit, the equivalent resistance of resistors in parallel can be calculated using the formula:

frac{1}{R_{parallel}} frac{1}{R_1} frac{1}{R_2}

For two 10Ω resistors:

frac{1}{R_{parallel}} frac{1}{10} frac{1}{10} frac{2}{10} frac{1}{5}

This gives us:

R_{parallel} 5Ω

Next, the total resistance of the circuit is the sum of the 6Ω resistor in series with the parallel combination:

R_{total} R_{series} R_{parallel} 6Ω 5Ω 11Ω

Step 2: Calculate Total Current

The total current in the circuit can be determined using Ohm's Law:

I frac{V_{source}}{R_{total}} frac{12V}{11Ω} approx 1.09A

Step 3: Calculate Voltage Drops

Voltage Drop Across the 6Ω Resistor

Using Ohm's Law again, the voltage drop across the 6Ω resistor can be calculated as:

V_{6Ω} I times R_{6Ω} 1.09A times 6Ω approx 6.54V

Voltage Drop Across the Parallel Resistors

The voltage drop across the parallel resistors is the difference between the total voltage and the voltage drop across the 6Ω resistor:

V_{parallel} V_{source} - V_{6Ω} 12V - 6.54V approx 5.46V

Voltage Drop Across Each 10Ω Resistor

Since the two 10Ω resistors are in parallel, the voltage drop across each resistor is the same:

V_{10Ω} V_{parallel} approx 5.46V

Summary of Results

Therefore, the voltage drop for both 10Ω resistors is approximately 5.46V, not 5.5V. The formulas used in this calculation are Ohm's Law and the formula for equivalent resistance of resistors in parallel.

Understanding these principles is essential for accurately assessing and designing electrical circuits. By mastering these calculations, you can ensure that your circuits function as intended and operate safely and efficiently.