Electric Circuits - Mission EC8 Detailed Help

A battery and a resistor are connected as shown in circuit X below. Another resistor is added as shown in circuit Y. The equivalent resistance of circuit X will be ___ that of circuit Y.

Equivalent Resistance in Parallel Circuits:
Parallel circuits are characterized by multiple pathways or branches through which charge flows. When additional resistors are placed within separate branches of a parallel circuit, additional pathways for charge flow are provided. Thus, the addition of more resistors (which also means additional pathways) has the effect of decreasing the overall resistance and increasing the overall current.

This question asks you to compare the equivalent resistance of two circuits with a different number of resistors. Circuit X contains a single resistor. Circuit Y contains two resistors connected in parallel. When resistors become connected in parallel, the overall resistance is decreased because of the presence of an additional pathway for charge flow. See Know the Law section.

We expect knowledge to be intuitive and reasonable. And when it comes to parallel circuits, students' expectations are often challenged due to the following counterintuitive claim: the addition of more resistors in a parallel circuit leads to a decrease in overall resistance. In other words: add more resistors and get less resistance. The explanation for this counterintuitive claim is best explained by an analogy of parallel circuits to an automobile toll way. On a toll way, it is the toll booths that offer resistance to the flow of cars. To increase the rate of car flow, the toll way authority often decides to add another toll booth. The addition of this toll booth in a separate pathway would cause the overall resistance to lessen and the rate of car flow to increase. Adding more toll booths (resistors) in separate branches results in less overall resistance. Now that makes sense!


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