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

The Correct Option is D

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