Rankers Physics

Combination of Resistors: Practice Problem & Solution

The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is $0.25 \Omega$. What will be the effective resistance if they are connected in series? (2021)
$0.5 \Omega$
$1 \Omega$
$4 \Omega$
$0.25 \Omega$

Solution Explained:

To solve this problem, we apply the core principles of Combination of Resistors. Understanding the underlying formula is key to arriving at the correct answer below:

Let the resistance of each individual wire be $R$. In parallel, the equivalent resistance is $R_{eq} = \frac{R}{4} = 0.25 \Omega$, which gives $R = 1 \Omega$. When these four wires are connected in series, the effective resistance is $R_s = 4R = 4(1) = 4 \Omega$.

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