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 ?

The correct option is 4 Ω.

Step-by-step Explanation:

Step 1: Understand the resistance of a single wire
Let the resistance of each of the four individual wires be $R$.
Since all four wires have equal length, equal cross-sectional area, and are made of the same material, they all have the same individual resistance $R$.

Step 2: Analyze the parallel connection
When these four identical wires are connected in parallel, their effective resistance ($R_p$) is given by the formula:

$\frac{1}{R_p}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R}=\frac{4}{R}$

Rearranging for $R_p$:

$R_p=\frac{R}{4}$

We are given that the effective parallel resistance $R_p=0.25\Omega$. Substituting this value:

$0.25\Omega =\frac{R}{4}$

Multiplying both sides by 4 gives the individual resistance of one wire:

$R=0.25\times 4=1\Omega$

Step 3: Calculate the effective resistance in series
When these same four wires are connected in series, their effective resistance ($R_s$) is the sum of their individual resistances:

$R_s=R+R+R+R=4R$

Substituting the value of $R=1\Omega$ into the equation:

$R_s=4\times 1\Omega =4\Omega$

Thus, the effective resistance of the series connection is 4 Ω.