Question: 18. 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?
(1) 0.25 \Omega
(2) 0.5 \Omega
(3) 1 \Omega
(4) 4 \Omega
Answer: Option (4)
Explanation:
Let the resistance of each identical wire be R.
When four identical resistances are connected in parallel, the equivalent resistance is given by R_p = \frac{R}{4}.
It is given that R_p = 0.25\,\Omega. Therefore, \frac{R}{4} = 0.25.
Solving this, R = 1\,\Omega.
When the four wires are connected in series, the equivalent resistance is the sum of individual resistances.
So, R_s = R + R + R + R = 4R.
Substituting R = 1\,\Omega, we get R_s = 4 \times 1 = 4\,\Omega.
Therefore, the effective resistance in series is 4\,\Omega,
and the correct answer is Option (4).