### Understanding Parallel Resistors#### Quiz Question:**3. Four unequal resistors are connected in a parallel with each other. Which one of the following statements is correct about this combination?**A) The equivalent resistance is less than that of the smallest resistor.B) The equivalent resistance is equal to the average of the four resistances.C) The equivalent resistance is midway between the largest and smallest resistance.D) The equivalent resistance is more than the largest resistance.E) None of the other choices is correct.---### Explanation:When resistors are connected in parallel, the total or equivalent resistance (\(R_{eq}\)) of the circuit can be found using the formula:\[\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}\]Given that \(R_1, R_2, R_3\), and \(R_4\) are all different and unequal resistors. - **Option A:** The correct statement is that the equivalent resistance (\(R_{eq}\)) of a parallel circuit is always less than the smallest individual resistance in the combination. This is due to the nature of the parallel resistance formula, which effectively distributes the total current across multiple paths, thus lowering the overall resistance even more than the smallest single path.- **Option B:** Incorrect, as taking an average of the resistances does not apply to parallel circuits since the equivalent resistance is derived from the reciprocal sum of the individual resistances.- **Option C:** Incorrect, because the equivalent resistance in a parallel combination is not a simple arithmetic mean but rather follows the reciprocal sum rule.- **Option D:** Incorrect, as the equivalent resistance can never be greater than the smallest resistor in a parallel configuration.- **Option E:** Incorrect, referring to all the other incorrect options.Therefore, the correct answer is **A) The equivalent resistance is less than that of the smallest resistor.**---### Additional Resources:For more comprehensive learning and practice problems, explore the following resources:- [Understanding Parallel Circuits](#)- [Practice Problems on Resistors in Parallel](#)*(Note: Resource links are placeholders and should lead to actual educational content in a real website.)*

We can solve this question by assuming resistances value such as: R1=2ohm, R2=4ohm, R3=6ohm,…

3. Four unequal resistors are connected in a parallel with each other. Which one of the foll owing statements is correct about this combinati on? A) The equivalent resistance is less than that of the smallest resistor. B) The equivalent resi stance is equal to the average of the four resistances. C) The equivalent resistance is midway between the largest and smallest resistance. D) The equivalent resi stance is more than the largest resistance. E) None of the other choices is correct.

3. Four unequal resistors are connected in a parallel with each other. Which one of the foll owing statements is correct about this combinati on? A) The equivalent resistance is less than that of the smallest resistor. B) The equivalent resi stance is equal to the average of the four resistances. C) The equivalent resistance is midway between the largest and smallest resistance. D) The equivalent resi stance is more than the largest resistance. E) None of the other choices is correct.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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