There is a circuit with just one 3 ohm resistor. There is another circuit with three 3 ohm resistors in parallel. What has greater resistance?

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BlackTom AI · Accepted Answer

Consider the two circuits described. In any circuit, resistance adds differently depending on whether components are in series or in parallel.
Option 1: 'one 3 ohm resistor' — this is simply a single resistor with resistance 3 Ω.
Option 2: 'three 3 ohm resistors set up in parallel' — for resistors in parallel, the reciprocal of the total resistance is the sum of the reciprocals of each resistance. Here, each resistor is 3 Ω, so 1/R_total = 1/3 + 1/3 + 1/3 = 1, giving R_total = 1 Ω. The parallel combination thus has a smaller resistance than any individual 3 Ω resistor.
Option 3: 'they are the same' — this would only be true if the parallel arrangement somehow yielded 3 Ω, which does not happen here since parallel reduces resistance, not increases it.
Option 4: 'it depends on the voltage source' — the resistance of a passive resistor network does not depend on the voltage source; resistance is a property of the components and their configuration, independent of the applied voltage.
In summary, when comparing a single 3 Ω resistor to three 3 Ω resistors in parallel, the parallel network has a lower equivalent resistance (1 Ω) than the single resistor (3 Ω). This makes the single 3 Ω resistor the circuit with greater resistance among the options.

Physics Honors-Henrikson Unit 11 and part of 12 Test part 1

There is a circuit with just one 3 ohm resistor. There is another circuit with three 3 ohm resistors in parallel. What has greater resistance?

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