In a parallel circuit, the total resistance (R_total) is calculated differently than in a series circuit. In a parallel circuit, the individual resistances are connected across the same voltage source, resulting in multiple paths for current to flow. To find the total resistance, you use the following formula:
1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ
where R₁, R₂, R₃, ..., Rₙ are the resistances of individual components connected in parallel.
Once you have summed the reciprocals of all individual resistances, you take the reciprocal of that sum to get the total resistance:
R_total = 1 / (1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ)
Let's go through an example:
Suppose you have three resistors in parallel with resistances of 4 ohms, 6 ohms, and 8 ohms. To find the total resistance:
1/R_total = 1/4 + 1/6 + 1/8
Calculating the sum of the reciprocals:
1/R_total = (3/12) + (2/12) + (3/24)
1/R_total = (8/12) + (3/24)
1/R_total = 11/24
Now, take the reciprocal of the sum:
R_total = 24/11 ohms ≈ 2.18 ohms (rounded to two decimal places)
So, the total resistance of the three resistors in parallel is approximately 2.18 ohms.