What is the value of the equivalent resistance for three resistors of 2 Ω, 4 Ω, and 6 Ω in parallel?

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Multiple Choice

What is the value of the equivalent resistance for three resistors of 2 Ω, 4 Ω, and 6 Ω in parallel?

When resistors are connected in parallel, the total conductance adds up, which makes the overall resistance smaller than any individual resistor. Use 1/R_eq = 1/R1 + 1/R2 + 1/R3. Compute: 1/R_eq = 1/2 + 1/4 + 1/6 = 0.5 + 0.25 + 0.1667 ≈ 0.9167. In exact fractions, that's 6/12 + 3/12 + 2/12 = 11/12, so R_eq = 12/11 ≈ 1.09 Ω. So the equivalent resistance is about 1.09 Ω, which is smaller than the smallest resistor (2 Ω). The value 6 Ω would not come from these three in parallel.

When resistors are connected in parallel, the total conductance adds up, which makes the overall resistance smaller than any individual resistor. Use 1/R_eq = 1/R1 + 1/R2 + 1/R3.

Compute: 1/R_eq = 1/2 + 1/4 + 1/6 = 0.5 + 0.25 + 0.1667 ≈ 0.9167. In exact fractions, that's 6/12 + 3/12 + 2/12 = 11/12, so R_eq = 12/11 ≈ 1.09 Ω.

So the equivalent resistance is about 1.09 Ω, which is smaller than the smallest resistor (2 Ω). The value 6 Ω would not come from these three in parallel.

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