Question

u be
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 -​

Answer 1

Answer:

25

Explanation:

We know that

$R = \frac{\rho L}{A}$

Let the length of original wire be L

Then length of each new wire is L/5

As $R \alpha L$ (R is directly proportional to L)

New Resistance = R/5

When we put these in parallel,

$\frac{1}{R'}= \frac{1}{R/5} + \frac{1}{R/5} +\frac{1}{R/5} +\frac{1}{R/5} +\frac{1}{R/5}$

⇒$\frac{1}{R'}  = \frac{5}{R} +\frac{5}{R} +\frac{5}{R} +\frac{5}{R} +\frac{5}{R}$

⇒$\frac{1}{R'} = \frac{25}{R}$

⇒$R' = \frac{R}{25}$

⇒R/R' = 25