## 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. **C****urrent (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). **T****otal 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.

## 2 Comments

6 years ago

Nicely worked out. For another example of ( generalized ) resistance including alternating current, capacitors and inductors see: Incredibility Powerful Resistance Calculator

6 years ago

Nice tutorial