Question 14 of 31intermediate🔧 ApplyMCQ1 mark

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 R/R' is –

Exercise: EXERCISES | Q: 1 | (Page Page 23)
For More Understanding

Explanation

Option D is correct. When a wire of resistance R is cut into five equal parts, each part has resistance R/5 (since resistance is directly proportional to length). When these five parts are connected in parallel, the equivalent resistance R' is calculated using the parallel combination formula. The ratio R/R' equals 25, as derived from the step-by-step calculation.

Solution Steps

  1. Step 1: When the wire of resistance R is cut into five equal parts, each part has resistance = R/5 (resistance is proportional to length).

  2. Step 2: When five resistors of resistance R/5 each are connected in parallel, using the formula 1/R' = 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5), we get 1/R' = 5/(R/5) = 25/R.

  3. Step 3: Therefore, R' = R/25.

  4. Step 4: The ratio R/R' = R/(R/25) = 25.

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