Mastering Series Circuit Calculations for the Journeyman Electrician Exam

Successfully passing the Journeyman Electrician exam requires a firm grasp of essential electrical theory, and chief among these are series circuit calculations. These calculations form the bedrock of circuit analysis, and proficiency is non-negotiable for any aspiring journeyman. A series circuit is characterized by a single path for current, where all components are connected end-to-end. The core principles involve calculating total resistance by summing all individual resistances (RT = R1 + R2 + …). Once total resistance is known, you can apply Ohm’s Law (I = V/R) to find the total current, which is constant throughout the circuit. From there, the voltage drop formula is used to determine the voltage across each individual component. Mastering the interplay between total resistance, current, and individual voltage drops is crucial, as many exam questions are built around these fundamental concepts, including applications of Kirchhoff’s Voltage Law (KVL).

What Defines a Series Circuit?

The defining characteristic of a series circuit is its single path for electron flow. Imagine a single-lane road where all traffic must follow the same route; this is analogous to how a series circuit operates. The definition of electrical current is the rate at which electric charge flows past a point in a circuit. In a series configuration, this current (measured in amperes) is the same through every component. If you were to measure the current at any point in a simple series circuit, the reading would be identical. This is a fundamental rule and a key differentiator when comparing a series vs parallel circuit, where current splits among multiple branches. For a deeper dive into the nature of charge flow, our guide to electric charge and current provides essential context. This concept also applies whether you’re working with direct current or alternating current, a topic further explored in our explanation of AC vs DC.

Core Formulas for Series Circuit Calculations

To succeed on the journeyman exam, you must have instant recall and an intuitive understanding of the four key formulas that govern series circuits. These formulas allow you to solve for any unknown variable when others are provided.

Total Resistance Calculation (RT)

In a series circuit, calculating the total opposition to current flow is straightforward. The total resistance calculation is simply the sum of all individual resistances in the circuit. Each resistor adds to the total load, making it progressively harder for current to flow. The formula is:

RT = R1 + R2 + R3 + …

Ohm’s Law for Series Circuits

Ohm’s Law for series circuits is the master key to unlocking other values. It defines the relationship between voltage (V), current (I), and resistance (R). Once you have calculated the total resistance (RT) and know the source voltage (VT), you can find the total current (IT) flowing through the entire circuit. The formula is:

IT = VT / RT

Because the series circuit current is constant everywhere, this value (IT) is the same current that flows through R1, R2, R3, and so on.

Kirchhoff’s Voltage Law (KVL) and Voltage Drop

Kirchhoff’s Voltage Law (KVL) states that the sum of all the individual voltage drops across the resistors in a closed loop is equal to the total source voltage. A “voltage drop” is the amount of voltage used up by a component as current passes through it. To find the voltage drop across any single resistor, you rearrange Ohm’s Law. This technique is often called resistor voltage division. The voltage drop formula for an individual resistor is:

V(resistor) = IT x R(resistor)

For example, the voltage drop across R1 is V1 = IT x R1. According to KVL, if you add up all the individual drops (V1 + V2 + V3…), the sum will equal your starting source voltage (VT).

Electrical Power Calculation

The final piece of the puzzle is the electrical power calculation, measured in watts (W). Power can be calculated for each component individually or for the entire circuit. The total power in a series circuit is the sum of the power dissipated by each individual resistor. The primary formulas for power are:

• P = V x I (Power = Voltage x Current)
• P = I² x R (Power = Current Squared x Resistance)
• P = V² / R (Power = Voltage Squared / Resistance)

To find the total power in series circuits, you can either use the total voltage, total current, and total resistance (e.g., PT = VT x IT) or calculate the power of each resistor and add them together (PT = P1 + P2 + P3…).

Step-by-Step Example: Solving a Typical Exam Problem

Let’s apply these principles to a problem similar to what a journeyman electrician might face on an exam. For more examples, see our detailed guide to journeyman electrician exam calculations.

Problem: A simple single-phase circuit has a source voltage of 120V connected to three resistors in series: R1 = 20Ω, R2 = 30Ω, and R3 = 50Ω. Find the total resistance, total current, the voltage drop across each resistor, and the total power dissipated.

1. Calculate Total Resistance (RT): Add all the resistor values.
   
   RT = 20Ω + 30Ω + 50Ω = 100Ω
2. Calculate Total Current (IT): Use Ohm’s Law with the total values.
   
   IT = VT / RT = 120V / 100Ω = 1.2A
3. Calculate Individual Voltage Drops: Use the total current (1.2A) and apply the voltage drop formula to each resistor.
   • V1 (across R1) = 1.2A x 20Ω = 24V
   • V2 (across R2) = 1.2A x 30Ω = 36V
   • V3 (across R3) = 1.2A x 50Ω = 60V
4. Verify with Kirchhoff’s Voltage Law (KVL): Sum the individual voltage drops to ensure they equal the source voltage.
   
   24V + 36V + 60V = 120V. The calculation is correct.
5. Calculate Total Power (PT): Use the total voltage and total current.
   
   PT = VT x IT = 120V x 1.2A = 144W

Ace your exam with targeted practice. Check out our online electrical courses and exam prep materials designed to help you master these critical calculations.

Connecting Theory to the NEC: Voltage Drop and Conductor Sizing

While theoretical calculations are vital, a licensed master electrician or journeyman must also apply these concepts practically according to the National Electrical Code (NEC). Understanding the relationship between circuit resistance and voltage drop is critical for proper conductor sizing for series circuits and ensuring code compliance.

The NEC provides recommendations for voltage drop in Informational Notes, such as in NEC 210.19(A) and 215.2(A). These notes suggest limiting voltage drop to 3% for a branch circuit and 5% for the total of a feeder and branch circuit combined. Excessive voltage drop can cause equipment to underperform and represents wasted energy.

The resistance of the wire itself contributes to the total resistance of the circuit and, therefore, the voltage drop. This resistance depends on the material (copper or aluminum), its length, and its cross-sectional area. This area is measured in Circular Mils (CM). To perform an accurate Circular Mils (CM) calculation or find a conductor’s properties, you must reference the official nec code book, specifically NEC Chapter 9, Table 8. This table provides the DC resistance for various conductor sizes, which is a crucial variable in professional voltage drop calculations.

Key Takeaways for Exam Day

• In a series circuit, current is constant through all components.
• Total resistance is the sum of all individual resistances.
• The sum of all voltage drops must equal the source voltage (Kirchhoff’s Voltage Law).
• Ohm’s Law for series circuits (V=IR) is the fundamental tool for finding unknown values.
• Be prepared to use NEC Chapter 9, Table 8 to find conductor resistance for voltage drop problems.

Frequently Asked Questions (FAQ)

What is the first step in solving series circuit calculations?

The first step in almost all series circuit calculations is to determine the total resistance (RT). You do this by adding the values of all individual resistors in the circuit (RT = R1 + R2 + R3…). Once you know the total resistance and the source voltage, you can find the total current, which unlocks the rest of the circuit’s values.

How does current behave in a series circuit?

The definition of electrical current is a flow of charge, and in a series circuit, that flow has only one path to follow. Therefore, the series circuit current is constant at every point. The current that leaves the positive terminal of the source is the same current that flows through each resistor and returns to the negative terminal.

Why is understanding the voltage drop formula important for a journeyman electrician?

A journeyman electrician must use the voltage drop formula (V = I x R) for two reasons. First, it’s essential for exam questions involving circuit analysis. Second, in the field, it’s used to ensure conductor sizes are adequate to prevent excessive voltage drop over long runs, which is critical for equipment performance and meeting NEC voltage drop limits recommendations.

Does the NEC specify a mandatory voltage drop limit?

No, the NEC voltage drop limits are primarily recommendations found in Informational Notes, not mandatory rules. For example, NEC 210.19(A) suggests a 3% drop for branch circuits and a 5% total drop for the feeder and branch circuit combined. While not strictly enforceable as code, adhering to these guidelines is a standard industry best practice and essential for proper electrical system design, making it a key part of modern electrician training.