How do you calculate total resistance in a parallel circuit?

To calculate total resistance in a parallel circuit, use the formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...

In a parallel circuit, the total resistance is not simply the sum of the individual resistances, as it is in a series circuit. Instead, the reciprocal (1 divided by the resistance) of the total resistance is equal to the sum of the reciprocals of each individual resistance. This is because, in a parallel circuit, the current has multiple paths to take, which effectively reduces the overall resistance.

Let's break it down with an example. Suppose you have three resistors in parallel with resistances of 6 ohms, 3 ohms, and 2 ohms. First, you take the reciprocal of each resistance:

1/6, 1/3, and 1/2.

Next, you add these reciprocals together:

1/6 + 1/3 + 1/2.

To add these fractions, you need a common denominator. The common denominator for 6, 3, and 2 is 6. So, convert each fraction:

1/6 remains 1/6,
1/3 becomes 2/6,
1/2 becomes 3/6.

Now, add them up:

1/6 + 2/6 + 3/6 = 6/6 = 1.

So, 1/R_total = 1. To find R_total, take the reciprocal of 1, which is simply 1 ohm. Therefore, the total resistance in this parallel circuit is 1 ohm.

This method works for any number of resistors in parallel. Just remember to take the reciprocal of each resistance, add them together, and then take the reciprocal of that sum to find the total resistance. This approach ensures you correctly account for the way current divides among the different paths in a parallel circuit.