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 $0.25\, \Omega$. What will be the effective resistance if they are connected in series?

• A. $0.25\, \Omega$
• B. $0.5\, \Omega$
• C. $1\, \Omega$
• D. $4\, \Omega$

Answer 1

The Correct Option is D

To determine the effective resistance when four wires are connected in series, we need to first understand the resistance calculations in both parallel and series circuits.

Given:

• Four identical wires in parallel have an effective resistance of \(0.25\, \Omega\).
• Each wire has the same resistance \(R\).

1. Calculate the resistance of a single wire:

When resistors are connected in parallel, the formula for effective resistance \( R_p \) is:

\(\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4}\)

Since all resistances are equal, \(R_1 = R_2 = R_3 = R_4 = R\), the equation simplifies to:

\(\frac{1}{R_p} = \frac{4}{R}\)

We know \(R_p = 0.25\, \Omega\), so:

\(\frac{1}{0.25} = \frac{4}{R}\)

\(R = 4 \times 0.25 = 1\, \Omega\)

Thus, the resistance of each wire is \(1\, \Omega\).

2. Calculate the effective resistance in series:

In series, the total resistance is the sum of all resistances:

\(R_s = R_1 + R_2 + R_3 + R_4\)

\(R_s = 1 + 1 + 1 + 1 = 4\, \Omega\)

Therefore, the effective resistance when the wires are connected in series is \(4\, \Omega\).

Conclusion: The correct answer is \(4\, \Omega\). None of the other options match the calculated effective resistance in a series connection.