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 ?

Correct Answer: 4 Ω

Step-by-Step Explanation:

Let the resistance of each of the four wires be represented by $R$ (since they have equal length, equal cross-sectional area, and are made of the same material, their individual resistances are identical).

1. Parallel Connection:
When $n=4$ identical resistors are connected in parallel, their equivalent resistance $R_p$ is given by the formula:
$\frac{1}{R_p}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\frac{1}{R}=\frac{4}{R}$
Taking the reciprocal, we get:
$R_p=\frac{R}{4}$

Given that the effective parallel resistance $R_p=0.25\Omega$, we can solve for $R$:
$0.25=\frac{R}{4}$
$R=0.25\times 4=1\Omega$
So, the resistance of each individual wire is $1\Omega$.

2. Series Connection:
When these four identical 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 this equation:
$R_s=4\times 1=4\Omega$

Thus, the effective resistance when connected in series will be 4 Ω.