Question

A technician has $10$ resistors each of resistance $0.1\Omega$. The largest and smallest resistance that he can obtain by combining these resistors are:

• A. $10\Omega \text{and}1\Omega$
• B. $1\Omega \text{and}0.1\Omega$
• C. $1\Omega \text{and}0.01\Omega$
• D. $0.1\Omega \text{and}0.01\Omega$

Answer 1

The correct option is C $1\Omega \text{and}0.01\Omega$

Given,

Number of resistors, $n=10$

Resistance of each resistors, $R=0.1\Omega$

For the largest resistance, all ten resistors should be connected in series.

The effective resistance of $n$ resistors having equal resistances $R$ in series,

$R_s=n\times R$

$R_s=10\times 0.1$

$R_s=1\Omega$

For the smallest resistance, all ten resistors should be connected in parallel.

The effective resistance of $n$ resistors having equal resistances $R$ in parallel,

$R_p=\frac{R}{n}$

$R_p=\frac{0.1}{10}$

$R_p=0.01\Omega$