Calculating the total resistance in a parallel circuit is simple if you know the right formula.

In a parallel circuit, different components, like resistors, are connected between the same two points. This setup lets the electric current travel through multiple paths.

To find the total resistance (which we call $R_t$) for resistors in parallel, you will use this formula:

$$\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots$$

Here, $R_1$, $R_2$, and $R_3$ are the resistances of each resistor.

Example:

Let’s say you have three resistors with these values:

• $R_1 = 4 \, \Omega$
• $R_2 = 6 \, \Omega$
• $R_3 = 12 \, \Omega$

Now, we will plug these numbers into the formula:

$$\frac{1}{R_t} = \frac{1}{4} + \frac{1}{6} + \frac{1}{12}$$

To solve this, we need to find a common denominator, which is 12:

$$\frac{1}{R_t} = \frac{3}{12} + \frac{2}{12} + \frac{1}{12} = \frac{6}{12}$$

Now, if we flip the equation, we get:

$$R_t = \frac{12}{6} = 2 \, \Omega$$

So, the total resistance in this parallel circuit is $2 \, \Omega$.

Keep in mind that the total resistance in a parallel circuit is always less than the smallest single resistor!