Calculating the Electrical Unknowns of a DC Series Circuit

This lesson will teach you how to calculate all the electrical unknowns of a DC Series Circuit, and is a companion to the lesson “Calculating the Electrical Unknowns of a DC Parallel Circuit.” We will examine the three laws of a series circuit, which will help explain how this type of circuit works, and Kirchhoff’s Voltage Law (KVL), which will help explain voltage drops in a closed loop circuit.

For Reference, Review, and Practice
Below are some helpful online references for further review and practice:

Figure 1. Three Automotive Bulb Filaments in a Series Circuit

In order to completely understand the function of a DC Series Circuit, all the electrical unknowns must be calculated mathematically. A Series Circuit is a complete circuit with more than one resistive load and only one path for current to flow (see circuit in Figure 1 above). Before we begin our analysis of this circuit, we must understand the symbols of its factors. Based upon Ohm’s Law, is for voltage (measured in volts), is for resistance (measured in ohms, and the symbol is Ω), is for current flow (measured in amperes), and is for power (measured in watts). See the companion lesson “Applying Ohm’s Law” for further instruction.

In this automotive application with three bulb filaments in a Series Circuit, the source voltage, or the Total Voltage (VT) is 12V DC. In order to understand this Series Circuit with three resistive elements, there are 12 unknowns, which must be calculated mathematically. We will use subscripts to help keep track of all the circuit elements. The 12 circuit elements or unknowns are as follows:

  • RT = Total Resistance
  • IT = Total Current flow
  • VR= Voltage Drop across R1
  • VR= Voltage Drop across R2
  • VR= Voltage Drop across R3
  • IR1 = Current flow through R1
  • IR2 = Current flow through R2
  • IR3 = Current flow through R3
  • PR1 = Power dissipated by R1
  • PR2 = Power dissipated by R2
  • PR3 = Power dissipated by R3
  • P= Total Power dissipated in the circuit

The Three Laws of a Series Circuit

The three laws that govern a Series Circuit are as follows:

Law #1 – The total resistance in a series circuit is the sum total of the individual resistances. The resistance values of each electrical load are simply added together.

Law #2 – The current flow is the same throughout the entire circuit.

Law #3 – The sum of the voltage drops in a series circuit will equal the source voltage (total voltage).

Kirchhoff’s Voltage and Current Laws

Kirchhoff’s Voltage Law (KVL): Applies to Series Circuits

The voltage around any closed circuit is equal to the sum (total voltage) of the voltage drops across the resistances in the closed loop.

The mathematics of this law is expressed in the equations below:

∑ ∆V = 0 (Note: The Greek letter Sigma “∑” means “summation in mathematics” and the

Greek letter Delta ∆ means “a change in”).

V1+ V2+ V= 0

VT = V1+ V2+ V3+ . . . + Vn

Kirchhoff’s Current Law (KCL): Applies to Parallel Circuits

The algebraic sum of all currents entering and exiting a node must equal zero.

The mathematics of this law is expressed in the equation below:

∑ IIn = ∑ IOut = 0

I1+ I2+ I3 – I– I– I= 0

Formulas to Know

(Note: These equations are listed in the order they should be used.)

Total Resistance: R= R1+ R2+ R3 . . .

Power dissipated across R1: PR1 = IRR1

Total Current: I= VT/RT, or I= IR1+IR2+IR3 . . .

Power dissipated across R2: PR2 = IRR2

Power dissipated across R3: PR3 = IRR3

Voltage Drop across R1: VR1 = IRx R1

Total Power: P= PR1+PR2+PR3 . . .

Voltage Drop across R2: VR= IRx R2

Voltage Drop across R3: VR3 = IRx R3

Current flow through R1: IR= VR1/R1

Current flow through R2: IR= VR2/R2

Current flow through R3: IR= VR3/R3


Directions: Review the image below and complete the “Learn by Doing” and” Did I Get This?” problems by clicking on the links below.

Figure 2. Three Automotive Bulb Filaments in a Series Circuit

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