The equivalent resistance of a 10 Ω resistor and a 30 Ω resistor connected in parallel is

Question

The equivalent resistance of a 10 Ω resistor and a 30 Ω resistor connected in parallel is

BlackTom AI · Accepted Answer

To approach the problem, I’ll first recall how to combine resistors in parallel. When resistors are in parallel, their conductances (the reciprocals of resistance) add: 1/R_total = 1/R1 + 1/R2.

Option A: 0.130 Ω. This value is far smaller than either individual resistor (10 Ω or 30 Ω). In a parallel connection, the equivalent resistance is always less than the smallest individual resistance, but 0.130 Ω would require a much larger combined conductance than 1/10 + 1/30 can provide. Specifically, 1/10 + 1/30 = 0.1 + 0.0333... = 0.1333..., which would give R_total ≈ 7.5 Ω, not 0.130 Ω. So this is incorrect.

Option B: 7.50 Ω. This is a plausible outcome because the formula gives 1/R_total = 1/10 + 1/30 = 0.1333..., and taking the reciprocal yields R_total = 7.5 Ω. Not only is this less than the smallest resistor (10 Ω), it matches the exact parallel calculation for 10 Ω and 30 Ω, making it the correct result.

Option C: 20 Ω. If the resistors were in series, you would get 10 Ω + 30 Ω = 40 Ω, not 20 Ω. In parallel, the equivalent is always less than the smallest resistance, so 20 Ω cannot arise from 10 Ω in parallel with 30 Ω. This makes it incorrect.

Option D: 40 Ω. This is the sum of the two resistances, which would occur if the resistors were connected in series, not in parallel. Since the question specifies parallel, this option misinterprets the connection and is therefore incorrect.

In summary, the correct approach shows that the parallel combination yields a total resistance less than the smallest resistor, computed via 1/R_total = 1/10 + 1/30, which gives R_total = 7.5 Ω. The remaining options fail due to not satisfying the parallel combination rule or due to misinterpreting the connection type.

APPHYSC142-031 with labs Exam Review - Final

The equivalent resistance of a 10 Ω resistor and a 30 Ω resistor connected in parallel is

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