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 find R/R’?

Answer 1

We know that, R ∝ l 

Initial resistance of the wire = RΩ 

When wire is cut into 5 pieces, its resistance will become 1/5^th . 

∴ resistance of each piece of wire after being cut into 5 pieces = \(\frac{R}{5}\)Ω 

Now, these wires are connected is parallel.

∴\(\frac{1}{R'}\) = \(\frac{1}{R_1} + \frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4}+\frac{1}{R_5}\) 

\(\frac{1}{R'}\) = \(\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}\) 

∴\(\frac{1}{R'}\)  = \(\frac{25}{R}\) 

∴\(\frac{R}{R'}\) = 25