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

Answer 1

The correct option is A $4\Omega$

All the wires are identical and of same material, so they will have the same value of resistance.

Let it be $R$, when these are (four) connected in parallel,


$R_p=\frac{R}{4}(\because \frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4})$

Given, $R_p=0.25\Omega$

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

$\therefore R=1\Omega$

Now, these four resistances are arranged in series


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

Hence, $\left(A\right)$ is the correct answer.