Question

The lowest resistance which can be obtained by connecting $10$ resistors each of $\frac{1}{10}\Omega$ is

• A. $1/250\Omega$
• B. $1/100\Omega$
• C. $1/200\Omega$
• D. $1/10\Omega$

Answer 1

The correct option is B $1/100\Omega$

The lowest resistance will be in the case when all the resistors are connected in parallel.

In parallel combination, we calculate the equivalent resistance $\left(R_{eq}\right)$ as

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}.........$

Where $R_1,R_2,R_3.....$ are the resistances that we are connecting in the parallel.

In our question, All the 10 resistors have a resistance of $\frac{1}{10}\Omega =0.1\Omega$

$\frac{1}{R_{eq}}=\frac{1}{0.1}+\frac{1}{0.1}.........10times$

$\frac{1}{R_{eq}}=10+\mathrm{10......10}times$

$\frac{1}{R_{eq}}=100$

$R_{eq}=\frac{1}{100}\Omega$