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QPage 196: Q1: HC Verma: Concepts of Physics - Volume 2 Electric Current in Conductors Page 196: Q1 Solution: Suppose you have three resistors, each of value . List all the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often overlook the two distinct mixed configurations (two in parallel with one in series, versus two in series with one in parallel) or mistakenly assume only pure series/parallel combinations are valid. To avoid this, systematically enumerate all unique circuit topologies by grouping resistors into sub-units before combining them.

Suppose you have three resistors, each of value 30 Ω30 \ \Omega. List all the different resistances you can obtain using them.

Step-by-Step Verified Solution

**Answer:** The different resistances that can be obtained using three 30 Ω30\ \Omega resistors are: 10 Ω10\ \Omega, 20 Ω20\ \Omega, 45 Ω45\ \Omega, 60 Ω60\ \Omega, and 90 Ω90\ \Omega. **Step-by-Step Explanation:** All three in series: R=30+30+30=90 ΩR = 30 + 30 + 30 = 90\ \Omega. All three in parallel: R=30/3=10 ΩR = 30/3 = 10\ \Omega. Two in parallel, then in series with the third: R=15+30=45 ΩR = 15 + 30 = 45\ \Omega. Two in series, then in parallel with the third: R=60∥30=20 ΩR = 60 \parallel 30 = 20\ \Omega. One resistor alone: R=30 ΩR = 30\ \Omega (but this uses only one resistor). The distinct values using all three are 10, 45, 90, and 20. If using a subset, 30 and 60 are also possible. The standard answer lists: 10, 20, 45, 90 [citation:2].

All Questions in this Chapter

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