Combination Of Resistors Series And Parallel

Given:
- Total resistance of the wire: $20%20%5C%2C%20%5COmega$
- The wire is divided into 10 equal parts.

Step 1: Resistance of each part
The resistance of each part is:

$R_%7B%5Ctext%7Bpart%7D%7D%20%3D%20%5Cfrac%7B%5Ctext%7BTotal%20resistance%7D%7D%7B%5Ctext%7BNumber%20of%20parts%7D%7D%20%3D%20%5Cfrac%7B20%20%5C%2C%20%5COmega%7D%7B10%7D%20%3D%202%20%5C%2C%20%5COmega.$

Step 2: Parallel combination of two parts
Each pair of two parts is connected in parallel. The equivalent resistance of a parallel combination is:

$R_%7B%5Ctext%7Bparallel%7D%7D%20%3D%20%5Cfrac%7BR_%7B%5Ctext%7Bpart%7D%7D%7D%7B2%7D%20%3D%20%5Cfrac%7B2%20%5C%2C%20%5COmega%7D%7B2%7D%20%3D%201%20%5C%2C%20%5COmega.$

Step 3: Total number of parallel combinations
Since there are 10 parts and they are paired in groups of 2, the total number of parallel combinations is:

$%5Ctext%7BNumber%20of%20parallel%20combinations%7D%20%3D%20%5Cfrac%7B10%7D%7B2%7D%20%3D%205.$

Step 4: Series combination of parallel pairs
The 5 parallel combinations (each of $1%20%5C%2C%20%5COmega$ ) are connected in series. The equivalent resistance of a series combination is:

$R_%7B%5Ctext%7Beq%7D%7D%20%3D%205%20%5Ctimes%20R_%7B%5Ctext%7Bparallel%7D%7D%20%3D%205%20%5Ctimes%201%20%5C%2C%20%5COmega%20%3D%205%20%5C%2C%20%5COmega.$

Thus, the equivalent resistance of the final combination is $R_%7B%5Ctext%7Beq%7D%7D%20%3D%205%20%5C%2C%20%5COmega$ .

To find the best combination of resistors with given resistance values to obtain an equivalent resistance of 6 Ω, let's analyze each configuration option:

Observe that we have resistors: $R_1%20%3D%20R_2%20%3D%20R_3%20%3D%205%20%5C%2C%20%5COmega$ and $R_4%20%3D%2010%20%5C%2C%20%5COmega$ .
The task demands achieving an equivalent resistance of 6 Ω using these resistors.
The provided correct circuit looks something like this:
The solution involves using the electrical arrangement via series and parallel combinations:
Specifically, when resistors $R_1$ , $R_2$ , and $R_3$ are connected in parallel:
Next, connect $R_4%20%3D%2010%20%5C%2C%20%5COmega$ in series with the calculated $R_%7B%5Ctext%7Bparallel%7D%7D$ .
The total resistance is thus calculated as:

On comparing and rechecking, if using these configurations won't yield 6.0 Ω, the depicted combination below potentially showcases the expected correct selection. Ensure to replicate these equations to sync with unit transformation or specific solution context:

About Combination Of Resistors Series And Parallel - JEE-MAIN

Combination Of Resistors Series And Parallel is a vital chapter for JEE-MAIN aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

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About Combination Of Resistors Series And Parallel - JEE-MAIN

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Why focus on Combination Of Resistors Series And Parallel PYQs?

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Combination Of Resistors Series And Parallel

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

About Combination Of Resistors Series And Parallel - JEE-MAIN

Frequently Asked Questions

Why focus on Combination Of Resistors Series And Parallel PYQs?

How to best use this analysis?

Chapter Questions
2 MCQs