Question

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 Ω. What will be the effective resistance if they are connected in series?

• A. 4 Ω
• B. 0.25 Ω
• C. 0.5 Ω
• D. 1 Ω

Answer 1

The Correct Option is A

To solve the problem, we need to understand the concepts of series and parallel resistances.

1. When resistors are connected in parallel, the reciprocal of the total or effective resistance \(R_{\text{parallel}}\) is given by the sum of the reciprocals of each individual resistance, \(R\):

\[\frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}\]

1. In this case, since all wires are identical, i.e., same resistance \(R\), the equation simplifies to:

\[\frac{1}{R_{\text{parallel}}} = \frac{4}{R}\]

1. Given that the effective resistance of parallel connection, \(R_{\text{parallel}}\), is 0.25 Ω:

\[\frac{1}{0.25} = \frac{4}{R}\]

1. Solving for \(R\), we get:

\[R = 4 \times 0.25 = 1 \, \Omega\]

1. Now, when the resistors are connected in series, the total or effective resistance \(R_{\text{series}}\) is simply the sum of individual resistances:

\[R_{\text{series}} = R_1 + R_2 + R_3 + R_4\]

1. Since all resistors have the same resistance \(R = 1 \, \Omega\) , the series resistance becomes:

\[R_{\text{series}} = 1 + 1 + 1 + 1 = 4 \, \Omega\]

1. Therefore, the effective resistance if the wires are connected in series is 4 Ω, which matches the correct option: 4 Ω.