Question

A wire of resistance R is cut into ten equal parts which are then joined in parallel. The new resistance is:

• A. 0.01 R
• B. 0. 1 R
• C. 10 R
• D. 100 R

Answer 1

The correct option is A 0.01 R

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 ten parts becomes resistors of resistance $\frac{R}{10}$each.
The recombination of $10$ resistors, each of resistance $\frac{R}{10}$, gives a resistor of equivalent resistance $R^{\prime }$ of value $\frac{\frac{R}{10}}{10}=\frac{R}{100}$
Hence,
$\frac{R^{\prime }}{R}=\frac{1}{100}$
Or,
$R^{\prime }=0.01R$