# 3 Ways to Calculate Series and Parallel Resistances

Do you need to learn how to calculate series, parallel, and network resistor associations that combine the two types? If you don't want to burn your circuit board, you need to know how! This article will show you how to do this in just a few steps. Before starting, it is worth remembering that the use of "input" and "output" in the manuals on the subject is just a picture of speech to help novices understand the concepts of connection between resistors. But actually they don't really have an "in" and an "out".

## Steps

### Method 1 of 3: Series Resistor Associations

#### Step 1. Understand what this means

The association of resistors in series consists of connecting the "output" of one resistor to the "input" of another in a circuit. Each additional resistor placed in a circuit adds up to the total resistance of that circuit.

• The formula for calculating a total of n resistors connected in series is:

Req = R1 + R2 + …. R

That is, the resistance values ​​of the resistors connected in series are simply added together. For example, if we were to find the equivalent resistance in the image below

• In this example, R1 = 100 Ω and R2 = 300Ω are connected in series. Req = 100 Ω + 300 Ω = 400 Ω

### Method 2 of 3: Associating Resistors in Parallel

#### Step 1. What is it

Parallel resistor association is when the "inputs" of 2 or more resistors are linked together, and the "outputs" of the resistors are linked together.

• The equation for a total of n resistors in parallel is:

Req = 1/{(1/R1)+(1/R2)+(1/R3..+(1/R)}

• Let's look at the following example. Data R1 = 20 Ω, R2 = 30 Ω and R3 = 30 Ω.

• The total equivalent resistance for the 3 resistors in parallel is:

Req = 1/{(1/20)+(1/30)+(1/30)}

= 1/{(3/60)+(2/60)+(2/60)}

= 1/(7/60)=60/7 Ω = approximately 8.57 Ω.

### Method 3 of 3: Circuits Combining Series and Parallel Resistor Associations

#### Step 1. What is it

A combined network is any combination of series and parallel circuits connected to form so-called "parallel equivalent resistors". Check out the example below.

• We can see that resistors R1 and R2 are connected in series. So their equivalent resistance (let's highlight it using Rs) is as follows:

Rs = R1 + R2 = 100 Ω + 300 Ω = 400 Ω.

• Next, we can see that resistors R3 and R4 are connected in parallel. So their equivalent resistance (let's highlight it using Rp1) is as follows:

Rp1 = 1/{(1/20)+(1/20)} = 1/(2/20) = 20/2 = 10 Ω

• So, we can conclude that resistors R5 and R6 are also connected in parallel. So their equivalent resistance (let's highlight it using Rp2) is as follows:

Rp2 = 1/{(1/40)+(1/10)} = 1/(5/40) = 40/5 = 8 Ω

• Now we have a circuit with resistors Rs, Rp1, Rp2 and R7 connected in series. Henceforth, they can be added together to obtain the equivalent resistance R7 of the network we had at the beginning of the process.

Req = 400 Ω + 20Ω + 8 Ω = 428 Ω.

## Interesting facts

1. Understand the resistance. Any material that conducts electrical current has resistivity, which is the resistance of a material to electrical current.
2. Resistance is measured in ohms. The symbol used for this measurement is Ω.
3. Strength properties vary by material.

• Copper, for example, has a resistivity of 0.0000017 (Ωcm).
• Ceramics, on the other hand, have a resistivity of around 10 14 (Ωcm).
4. The higher the number, the greater the resistance to electrical current. You can see that copper, which is commonly used in electrical wiring, has a very low resistivity. Ceramic, on the other hand, is so resistive that it serves as an excellent insulator.
5. How you join wires of varying resistances makes a big difference to the overall performance of a resistive network.
6. V=IR. This is Ohm's law, defined by Georg Ohm in the early 1800s. If you know the value of at least two of the variables in this equation, you can easily calculate the value of the third.

• V=IR: Voltage (V) is the product of current (I) x resistance (R).
• I=V/R: Current is the quotient of voltage (V) ÷ resistance (R).
• R=V/I: Resistance is the quotient of voltage (V) current (I).

## Tips

• Remember: when resistors are in parallel, there are many different paths to an end, so the total resistance will be less than each path. When the resistors are in series, current will have to travel through each resistor, so the individual resistors will be added together to give the total resistance for the series.
• The equivalent resistance (Req) is always less than the smallest contributor to a parallel circuit, and it is always greater than the largest contributor to a series circuit.