Question

A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R′, then the ratio $\frac {R}{R^′}$ is –

• A. $\frac {1}{25}$
• B. $\frac 15$
• C. 5
• D. 25

Answer 1

Answer: (D)

25

Answer 2

Resistance of a piece of wire is directly proportional to its length. If the piece of wire has a resistance R and the wire is cut into five equal parts. The resistance of each part = $\frac R5$
All the five parts are connected in parallel. Hence, equivalent resistance (R′) is given as
$\frac {1}{𝑅^′}=\frac {1}{\frac R5}+\frac {1}{\frac R5}+\frac {1}{\frac R5}+\frac {1}{\frac R5}+\frac {1}{\frac R5}$

⟹$\frac {1}{𝑅^′} =\frac 5R+\frac 5R+\frac 5R+\frac 5R+\frac 5R=\frac {25}{R}$

⟹$𝑅^′=\frac {𝑅}{25}$

⟹$\frac {𝑅^′}{𝑅}=25$

Hence, the correct option is (D): 25