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Step-by-Step Solution
Step 1: Identify the Resistance of Each Wire
We are given that four identical wires, each having the same length, cross-sectional area, and material, are connected in parallel. The equivalent (combined) resistance of this parallel configuration is 0.25$\,\Omega$. Since these four wires are identical and connected in parallel, their individual resistances will each be the same value, say $R$. For four identical resistors in parallel, the effective resistance $R_\text{parallel}$ is given by:
$ \frac{1}{R_\text{parallel}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{4}{R} $
Hence, we have:
$ R_\text{parallel} = \frac{R}{4}
= 0.25 \,\Omega
$
From this, solving for $R$ (the resistance of each individual wire) yields:
$ \frac{R}{4} = 0.25 \implies R = 0.25 \times 4 = 1 \,\Omega.
$
Step 2: Compute the Equivalent Resistance in Series
Next, we are asked to find the total resistance when these four wires are connected in series. For a series connection of resistors, the total or equivalent resistance $R_\text{series}$ is simply the sum of the individual resistances:
$ R_\text{series} = R + R + R + R = 4R.
$
Since we have found $R$ to be 1$\,\Omega$, substituting this in gives:
$ R_\text{series} = 4 \times 1 \,\Omega = 4 \,\Omega.
$
Step 3: State the Final Answer
Therefore, the effective resistance of the four identical wires when connected in series is 4$\,\Omega$.
