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A wire of resistance R1 is cut into five equal pieces. These five pieces of wire are then connected in parallel. If the resultant resistance of this combination be R2, then ratio R1/R2 is _______.
1. 1/25
2. 1/5
3. 5
4. 25

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Correct Answer - Option 4 : 25

The correct answer is 25.

  • R1​ is cut into 5 pieces. Resistance if each piece =R1​/5​
  • When connected in parallel net resistance unit be R1/5/5​​
  • R2​=R1​/25​
  • Now, ​R−1/R2​= R1​​/R1/25 ​​=25
  • Hence, the answer is 25.

  • Given: A wire of resistance R1 is cut into five equal pieces.
  • Then each piece has a resistance of
  • Then each piece has a resistance of \(\dfrac{R1}{5}\)
  • And given that the resultant resistance of this combination be R2.
  • Then the parallel combination is given by
  •  \(\dfrac{1}{R2} = \dfrac{1}{\dfrac{R1}{5}} + \dfrac{1}{\dfrac{R1}{5}}+ \dfrac{1}{\dfrac{R1}{5}} + \dfrac{1}{\dfrac{R1}{5}} + \dfrac{1}{\dfrac{R1}{5}}\)
  • \(\dfrac{1}{R2} = \dfrac{5}{R1} + \dfrac{5}{R1} + \dfrac{5}{R1} + \dfrac{5}{R1} + \dfrac{5}{R1} \)
  • \(\dfrac{1}{R2} = \dfrac{25}{R1}\)
  • \(\dfrac{R1}{R2}=25\)

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