Which is correct in reference to electrical resistance?

Question

BlackTom AI · Accepted Answer

Question restatement: Which is correct in reference to electrical resistance?
Options:
1) Two electrical devices will have the same combined resistance if they are connected in series as they will have if they are connected in parallel.
2) An electrical device that has a high resistance will use more power than one with a low resistance with the same applied voltage.
3) If one of three bulbs in a parallel lighting circuit is removed, the total resistance of the circuit will become greater.

Option 1 analysis: This statement claims that two devices in series will have the same combined resistance as in parallel. In reality, series and parallel configurations produce different total resistances. For series, the resistances add: R_total = R1 + R2 + ...; for parallel, the reciprocals add: 1/R_total = 1/R1 + 1/R2 + ... . These expressions show the total resistance is generally different between the two configurations, unless in a highly specific and uncommon set of values. Therefore, this option is false.

Option 2 analysis: Power in an electrical device under a fixed voltage is given by P = V^2 / R. A higher resistance R yields a smaller power for the same voltage, not a higher power. Thus, this option contradicts the fundamental relation between resistance and power and is incorrect.

Option 3 analysis: In a parallel circuit, each device (e.g., bulb) has the same voltage across it, and the total conductance (the reciprocal of resistance) is the sum of the individual conductances. When you remove one branch, you remove its conductance from the sum, so the overall equivalent resistance increases. Hence, the total resistance becoming greater when one parallel branch is removed is correct.

Summary: By comparing the statements, Option 3 correctly describes the behavior of resistance in a parallel circuit, while Options 1 and 2 contain incorrect claims about series versus parallel resistances and the relationship between resistance and power.

Which is correct in reference to electrical resistance?单项选择题

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