## Introduction: How to Solve a Basic Parallel or Series Circuit

When it comes to electrical engineering, solving circuits is a fundamental skill. Before beginning this instructable it is important to note the three main aspects of a circuit being current, voltage, and total resistance. Current (I) is how much physical electricity is running through each wire, which is measured in Amps. Potential difference, aka voltage (V) is measured in Volts, which is essentially the potential a circuit has to push electricity through the wire(s). Total resistance (R), measured in Ohms, is how much the circuit is resisting the flow of electricity. An entire circuit is shown in Fig. 1. Through this instructable you will learn how to solve for the total resistance of a circuit and then by using Ohm’s Law (I=V/R) to solve for the current (I) that a circuit will use.

Assumptions:

This instructable requires the basic knowledge of algebra along with the ability to use a calculator to solve algebraic equations. At Table 1 you can find tips for calculating the math values required in this instructable.

## Step 1: Identify the Voltage (V) of the Circuit and Recognize the Type of Resistance

The voltage of a circuit is displayed by the symbol found in Fig. 1.You can simply transcribe this value and keep it until we are solving for current (I) in Step 3.

A Resistor is a small component of a circuit used to change how much resistance is within the circuit. It is illustrated as such in Fig. 2.These resistors can be organized in two basic ways, either in parallel or in series.

Parallel:

Parallel resistors look like a “ladder” on a circuit, each one is stacked on top of each other so to speak. This is illustrated in Fig. 3.

Series:

Series resistors look like a “string” on a circuit, each one is placed end-to-end in a row, all traveling in the same direction. This can be seen in Fig. 4. Look at the circuit you are given and identify which type of resistance your circuit uses, then you may proceed to step 2.

## Step 2: Finding the Total Resistance

Because Ohm’s Law is found to be “I=V/R”, then we need one single, total value for resistance (R).

Series:

To find the total resistance of a series configuration, you simply add them together. For example, if you have three resistors R1, R2, and R3, the total resistance is as such “R=R1+R2+R3”. This is illustrated in Fig. 5.

Parallel:

To find the total resistance of a parallel configuration, we must divide one by each resistor value separately, add them together, then divide one by this total. Such as (1/R1 + 1/R2 + 1/R3) = 1/R ==> R=___. This is illustrated by Fig. 6. If you would like assistance with how to type these values into a calculator, please see Table 1.

## Step 3: Solve for Current (I)

Once you have found the total resistance (R) and given voltage (V) we plug it into the Ohm’s Law equation (I=V/R). For example if our voltage was 4 Volts and our total resistance was 9 Ohm’s, then our current (I) would be 4/9 Amps, which is equal to 0.4444 Amps. Please see Fig. 7 for an illustration of this method.

## Step 4: Try It for Yourself

As seen in Figures 8-11 there are four circuit examples.

Feel free to try each example while going through this instructable. The correct values for each example are found in Table 2 below.