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 R/R' is − (a)1/25 (b)1/5 (c) 5 (d) 25

Answer 1

Hey Dear,

◆ Answer - (d)

R/R' = 25

● Explanation -

Let l & A be length and cross sectional area of original wire.

R = ρl/A

When the wire is cut into 5 pieces, resistance of each piece will be -

R* = ρ(l/5)/A

R* = ρl/5A

When all these pieces are connected in parallel, equivalent resistance is given by -

R' = R*/5

R' = (ρl/5A)/5

R' = ρl/25A

R' = R/25

R/R' = 25

That's your answer. Hope this helps you..

Answer 2

Answer:

The ratio is 25. Thus, the correct answer is (D).

Explanation:

Piece of wire whose resistance is proportional to the wire length. In the question, resistance of the wire is given that is ‘’R’’. After that this wire is cut equally into the five pieces. So, each piece has the resistance of R/5. They are connected in parallel as mentioned in the question.

$\frac {1}{R_a} = \frac{5}{R} +\frac{5}{R} + \frac{5}{R} +\frac{ 5}{R} + \frac{5}{R}\\\\\frac {1}{R_a} =\frac { 5 + 5 + 5 + 5 +5}{R}\\\\\frac {1}{R_a} = \frac {25}{R}\\\\\frac {R}{R_a} = 25$