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Which One Doesn't Belong? - Equivalent Resistance - help11

When two or more resistors are placed in a circuit, it is common to describe their combined effect by comparing them to the effect of a single resistor. The equivalent resistance of such a circuit is the resistance that a single resistor would have in order to match the combined effect of all the resistors in that circuit. For instance, suppose that a parallel circuit having an equivalent resistance of 15 Ω were compared to a circuit with a single resistor having a resistance of 15 Ω; the two circuits would be equivalent to one another in terms of their effect upon the electric current.

There are three similar versions of this question. Here is one of the versions:

Version 1:

One of these circuits has an equivalent resistance that is not like the others. Which one doesn't belong?

Equivalent Resistance in a Parallel Circuit
When there are two or more resistors wired together in a parallel arrangement, the overall resistance to charge flow is less than the resistance of the lowest-resistance resistor. As discussed in the Fundamentals section (above), the equivalent resistance of such a circuit is the resistance that a single resistor would have in order to match the combined effect of all the resistors in that circuit. There is a fancy equation for calculating the equivalent resistance of parallel resistors. But for this Concept Builder, there is a far easier way. Read on ...

Suppose there is a circuit with two 12-Ω resistors with a parallel arrangement. Any given charge circulating through the circuit will only pass through one of these resistors. Half the circulating charge will pass through one resistor and half will pass through the other resistor. In such a parallel arrangement, the two 12-Ω resistors have a combined effect of 6 Ω. It's odd math, but for parallel circuits 12 Ω and 12 Ω is equivalent to 6 Ω. Similarly, 10 Ω and 10 Ω in parallel are equivalent to 5 Ω.

What if there are three 12-Ω resistors in a parallel circuit? The logic remains the same. Only one-third of the charge encounters any one of the 12-Ω resistors. And so the equivalent resistance is 4 Ω (one-third of the 12 Ω). It's odd math again, but for parallel circuits 12 Ω and 12 Ω and 12 Ω is equivalent to 4 Ω.

Try this link to The Physics Classroom Tutorial for more help with equivalent resistance in a parallel circuit:

Parallel Circuit