Question

How do you calculate total resistance in a parallel circuit?

Answer 1

In a parallel circuit, the total resistance (R_total) is calculated differently than in a series circuit. In a parallel circuit, the current has multiple paths it can take, and the total resistance is lower than the individual resistances.

To calculate the total resistance in a parallel circuit, you use the following formula:

1 / R_total = 1 / R1 + 1 / R2 + 1 / R3 + ... + 1 / Rn

Where:

R_total is the total resistance of the parallel circuit.
R1, R2, R3, ... Rn are the individual resistances of each component in the parallel circuit.

To get the reciprocal of each individual resistance, you take the inverse (1/Rn) of each resistance value and then add them together. Finally, take the reciprocal of the sum to get the total resistance (R_total).

Alternatively, you can use this formula to calculate the total resistance:

R_total = 1 / (1/R1 + 1/R2 + 1/R3 + ... + 1/Rn)

Let's go through a simple example to illustrate how to calculate the total resistance in a parallel circuit:

Suppose you have three resistors in parallel with the following values:
R1 = 4 ohms
R2 = 6 ohms
R3 = 10 ohms

Using the formula:
1 / R_total = 1 / 4 + 1 / 6 + 1 / 10

Now, calculate the sum of the reciprocals:
1 / R_total = 0.25 + 0.16667 + 0.1

Add them together:
1 / R_total = 0.51667

Now, calculate the reciprocal of the sum to find the total resistance (R_total):
R_total = 1 / 0.51667 ≈ 1.936 ohms

So, the total resistance of the parallel circuit is approximately 1.936 ohms. As you can see, the total resistance is less than the smallest individual resistance, which is a characteristic of parallel circuits.