(d) The student connects the two resistors in the diagram above in parallel. What happens to the total resistance of the circuit? Tick one box. It decreases square It increases square It does not change square Give a reason for your answer. qquad qquad

Question

Question

(d) The student connects the two resistors in the diagram above in parallel. What happens to the total resistance of the circuit? Tick one box. It decreases square It increases square It does not change square Give a reason for your answer. qquad qquad

Answer 1

[It decreases]

Answer 2

## Step 1: To solve this problem, we need to first review what parallel circuits are like. In a parallel circuit, several smaller conductive paths are branched off a main theme, allowing the current a number of different pathways through which to run. Devices connected in or making up these paths should not only have the same voltage across them but are also helpful for preventing full circuit failure should one part stop functioning normally. ## Step 2: Next, let's apply this knowledge to the problem at hand. Because the student has chosen to connect the two resistors in parallel, these two will be positioned in branches coming off from the main circuit—the overall route current follows from and back to its source. This design makes it possible to provide both the resistors with an equal voltage, each possessing but drawing this value apart from the other along their individual structured setups. ## Step 3: And now symbology-wise, let's not ignore that thing to masters like quantities—none other than mathematical operators. Total resistance (\(R_{total}\)) observed in parallel-linked circuits typically aligns with the formula: ### \(\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n} \) Where \(R_1, R_2, \cdots, R_n\) represent resistance individual resistors provide. All together their fully amassed divided forms fold into a counter operation specific to this setup so that mathematically too, we prove parallel circuits' resistance leans toward lesser rather than more values where laws hold proper. ## Step 4: According to the formula above, the total resistance is composed by adding up the reciprocal values. Once more resistors are connected in parallel, we simply add additional terms to the formula. Thus, having more resistors connected in parallel will decrease the total resistance.

Question

(d) The student connects the two resistors in the diagram above in parallel. What happens to the total resistance of the circuit? Tick one box. It decreases square It increases square It does not change square Give a reason for your answer. qquad qquad

Answer

Answer

Explain

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