In a parallel circuit, the total resistance is always lower than the smallest individual resistance.

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Multiple Choice

In a parallel circuit, the total resistance is always lower than the smallest individual resistance.

In a parallel circuit, there are multiple paths for current to flow, so the overall resistance decreases when you add more branches. The total resistance is found from 1/R_total = 1/R1 + 1/R2 + ..., which means adding another path increases the sum on the right, making 1/R_total larger and R_total smaller. Therefore, the total resistance is always less than any individual branch resistance (as long as there are at least two finite resistors). For example, two resistors of 6 Ω and 3 Ω in parallel give R_total = 1/(1/6 + 1/3) = 2 Ω, which is smaller than both 6 Ω and 3 Ω. Note that if there’s only one path (no parallel branches), the total equals that resistance, but with multiple parallel branches, the total is definitely lower than the smallest branch. Hence the statement is true.

In a parallel circuit, there are multiple paths for current to flow, so the overall resistance decreases when you add more branches. The total resistance is found from 1/R_total = 1/R1 + 1/R2 + ..., which means adding another path increases the sum on the right, making 1/R_total larger and R_total smaller. Therefore, the total resistance is always less than any individual branch resistance (as long as there are at least two finite resistors). For example, two resistors of 6 Ω and 3 Ω in parallel give R_total = 1/(1/6 + 1/3) = 2 Ω, which is smaller than both 6 Ω and 3 Ω. Note that if there’s only one path (no parallel branches), the total equals that resistance, but with multiple parallel branches, the total is definitely lower than the smallest branch. Hence the statement is true.

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