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 0.25Ω. What will be the effective resistance if they are connected in series?

(1) 0.25Ω

(2) 0.5Ω

(3) 1Ω

(4) 4Ω

Answer 1

Correct option is (4) 4Ω

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,

\(R_P = \frac R4\)  \(\left(\because \frac 1{R_p} = \frac{1}{R_1} +\frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4} \right)\)

Given, R_p = 0.25 Ω

∴ 0.25 = \(\frac R4\)

∴ R = 1Ω

Now, these four resistances are arranged in series

R_s = R + R + R + R

= 4R

= 4 × 1

= 4Ω

Answer 2

Option : (4) 4Ω

R_|| = \(\frac{R}{4}\) = 0.25Ω

R = 1Ω

Rseries = 4R 

= 4(1) 

= 4Ω.