Calculating total resistance in circuits can be pretty easy once you understand it! Let's look at how to do this for both series and parallel circuits.

Series Circuits:

In a series circuit, all the resistors are connected one after the other.

To find the total resistance (we'll call it $R_{total}$), you just add up all the individual resistances. You can use this formula:

$$R_{total} = R_1 + R_2 + R_3 + ... + R_n$$

For example, if you have two resistors, one with 4 ohms and another with 6 ohms, you would calculate:

$$R_{total} = 4 + 6 = 10 \, \Omega$$

Parallel Circuits:

Parallel circuits are a bit different. In these circuits, the resistors are connected across the same voltage source.

To find the total resistance for a parallel circuit, you use this formula:

$$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}$$

For example, if you have two resistors, one at 4 ohms and another at 6 ohms, you would calculate:

$$\frac{1}{R_{total}} = \frac{1}{4} + \frac{1}{6}$$

Doing this math, you find that the total resistance is about $2.4 \, \Omega$.

With these simple rules, you’ll be finding total resistance like a pro in no time!