Understanding the Voltage Across Series Resistors

This article aims to explain the concept of voltage distribution across resistors in a series configuration. We will explore how to calculate the voltage drop across individual resistors when they are connected in series with a DC power source.

The Concept of Series Resistors in a DC Circuit

When resistors are connected in a series configuration, they essentially form a chain where the current has only one path to follow. In such a setup, the current that flows through each resistor is identical. Additionally, the total resistance (Req) is the sum of individual resistances. This means that if you have two resistors, R1 and R2, connected in series, the equivalent resistance is calculated as:

Equivalent Resistance

Formula: Req R1 R2

Example: If R1 10 Ω and R2 20 Ω, then Req 10 Ω 20 Ω 30 Ω

Calculating the Current in the Circuit

Once the equivalent resistance is known, the current (I) flowing through the circuit can be calculated using Ohm's law, which states:

Formula: I V / Req

Example: If the source voltage (V) is 20 V, then the current (I) is:

I 20 V / 30 Ω 2/3 A

Understanding the Voltage Drop Across Individual Resistors

In a series circuit, the voltage drop across each resistor can be calculated using the voltage division rule. According to this rule, the voltage drop across a resistor is directly proportional to its resistance. The voltage drop (VR1) across the 10 Ω resistor can be calculated as follows:

Calculating Voltage Drop

Formula: VR1 I × R1

Example: VR1 (2/3 A) × 10 Ω 20/3 V 6.67 V

Similarly, the voltage drop (VR2) across the 20 Ω resistor is:

Formula: VR2 I × R2

Example: VR2 (2/3 A) × 20 Ω 40/3 V 13.33 V

Verification Using Kirchhoff's Voltage Law (KVL)

To confirm the calculations, Kirchhoff's Voltage Law (KVL) can be applied. According to KVL, the sum of the voltages around any closed loop in a circuit must be zero. In a series circuit, this means that the sum of the voltage drops across each resistor must equal the total voltage of the source.

KVL Calculation

Formula: Vtotal VR1 VR2

Example: Vtotal 6.67 V 13.33 V 20 V

Conclusion

By understanding the principles of series resistors and applying the voltage division rule, we can accurately calculate the voltage drop across individual resistors. Using KVL ensures that our calculations adhere to the fundamental principles of electrical circuits. This knowledge is crucial for designing and analyzing complex electrical circuits in various engineering and technological applications.