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

The correct option is D 25

We know,
1.When a resistance is divided into n identical resistances, each of resistance (say R') become $\frac{R}{n}$.
2.When n identical resistors each of resistance R', are connected in parallel, the equivalent resistance is $\frac{R^{\prime }}{n}$
The resistor R ,when divided into five parts become resistors of resistance $\frac{R}{5}$each.
The recombination of five resistors, each of resistance $\frac{R}{5}$, gives a resistor of equivalent resistance R' of value $\frac{\frac{R}{5}}{5}=\frac{R}{25}$
Hence,
$\frac{R}{R^{\prime }}=\frac{25}{1}$