# Solving a Simple Circuit Diagram With a Single Voltage Source and Resistors in Series and Parallel

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## Introduction: Solving a Simple Circuit Diagram With a Single Voltage Source and Resistors in Series and Parallel

Mechanical engineers require some basic knowledge of circuitry, electricity and related concepts in order to work cross-platform with electrical engineers, electricians, computer engineers and other related professionals. This Instructable will help one solve and learn one of the foundations of electrical circuits. We will work through the process of solving a circuit with a single voltage source and sets of resistors in series and parallel.

## Step 1: Draw a Diagram or Use the One Provided

• Distinguish between two elements with the same function (e.g. resistors, noted by the jagged sections) by giving each a different subscript label (X_1 notes the 1 is a subscript to X)
• Label each element with its name (e.g. R_1, R_2, etc.) and known value(s). In this case, the problem will provide the voltage of the voltage source and the resistance of each resistor.

## Step 2: Reduce Sets of Resistors Into One Equivalent Resistor

To find the equivalent resistance, take a set of resistors in series or parallel and reduce them to one equivalent resistor using the following rules.

• For resistors in series, add the resistance values of each resistor. R_t= R_1 + R_2 + R_3 + ...
• For resistors in parallel, use the equation 1/R_t = 1/R_1 + 1/R_2 + 1/R_3 + ... to solve for the equivalent resistance.

## Step 3: Draw a New Diagram With the New, Reduced Equivalent Resistor

• Draw a new circuit diagram with the newly reduced equivalent resistor.
• Keep the diagrams on hand; you will need them later to work back up and solve for the information needed.

## Step 4: Repeat Steps 2 and 3 Until One Equivalent Resistor Remains

• Repeat the process of reducing using the rules in Step 2 and drawing a further reduced circuit diagram.
• Continue until only one resistor, equivalent to the entire circuit, and the voltage source remain.

## Step 5: Calculate the Total Current of the Circuit

Use the formula V_s = I_t * R_eq to calculate the total current of the circuit.

• V_s represents the voltage of the voltage source.
• I_t represents the total current running in the circuit.
• R_eq represents the equivalent resistance of the whole circuit.

## Step 6: Work Back Up the Diagrams With the Information From the Reduced Equivalent Circuit to Solve for the Power, Current and Voltage Consumption of Each Resistor

• Use the information from the reduced equivalent circuit to calculate information about each resistor, both real and reduced.

Split consolidated equivalent resistors back into their original components. Use Kirchhoff's Rules (below) to gain information necessary to solve for each resistor's unknowns.

• Resistors in series with each other have the same current.
• Resistors in parallel with each other have the same voltage.

## Step 7: Check the Values Calculated for Each Resistor's Voltage and Current

Use the following rules to check your numbers each time you solve a reduced circuit or the original circuit.

• The sum of all voltages flowing through each resistor or parallel set of resistors should equal the voltage of the voltage source. Make sure to count each parallel set once in your calculations since each resistor in a parallel set has the same voltage as the others.
• In a parallel set, the sum of the currents flowing through all resistors in the set should equal the total current flowing through the set. In this case, it should equal the total current of the circuit.

## Step 8: Repeat Steps 6 and 7 for Each Diagram

• Work your way back up to the original diagram.
• Solve for voltage and current for each reduced resistor split into its original components using V = I * R for each individual resistor.
• Check each voltage total against the voltage source and each current total against the current flowing into the parallel set.
• If the problem requires power calculations: Calculate power using P = I^2 * R or P = I * V (I^2 denotes current squared).
• Stop when you obtain all necessary information regarding anywhere between one resistor and every resistor.