Question

The smallest resistance which can be obtained with ten $0.1$ ohm resistors is
A. 1 ohm
B. 0.1 ohm
C. 0.01 ohm
D. 0.001 ohm

Answer 1

Hint: Above question deals with the hindrances caused to the flow of electric current i.e., resistance. In order to solve the question, we must first be clear about the resistance and the ways in which the resistance can be applied. By selecting a suitable way (according to our question) and simplifying the values will lead to the answer.

Complete step by step answer:
Resistance can be briefed as the hindrance caused to the flow of electric current. It generally occurs due to the material used to transfer the electric current. Besides this the dimension of conductor can vary the amount of resistance caused by the material of conductor. In an electric circuit the resistors can be used in two formats, one in series and other one in parallel. In a series circuit, the equivalent resistance of all resistors is by directly adding the total resistance. In a parallel circuit, the equivalent resistance of all resistors is by fractional addition of resistance.

As parallel connection involves the fractional addition, hence the equivalent resistance in parallel connection is generally reduced. As the statement of our question requires to generate a minimum resistance, we need to arrange all resistors in parallel to yield minimum resistance. In parallel arrangement,
\[\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + ............ + \dfrac{1}{{{R_n}}}\]
Where, ${R_{eq}}$ = equivalent resistance and ${R_1},{R_2},.........{R_n}$= various resistance added in parallel in electric circuit

We have 10 resistors of 0.1ohm resistance, and to generate minimum resistance from them we will arrange them in parallel. On arranging them in parallel the equivalent resistance will be,
$\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{0.1}} + \dfrac{1}{{0.1}} + \dfrac{1}{{0.1}} + \dfrac{1}{{0.1}} + \dfrac{1}{{0.1}} + \dfrac{1}{{0.1}} + \dfrac{1}{{0.1}} + \dfrac{1}{{0.1}} + \dfrac{1}{{0.1}} + \dfrac{1}{{0.1}}$
Equating above equation,
$\dfrac{1}{{{R_{eq}}}} = 10\left( {\dfrac{1}{{0.1}}} \right)$
Substituting above equation,
$\dfrac{1}{{{R_{eq}}}} = 100$
$\Rightarrow {R_{eq}} = \dfrac{1}{{100}} \\
\therefore {R_{eq}} = 0.01\,\Omega $
Minimum resistance that can be generated from 10 resistors of resistance 0.1ohm is 0.01 ohm.

Therefore, the correct answer is option C.

Note: Resistance in mathematical form is explained as the ratio of potential applied to the electric current produced i.e., resistance is equal to the potential difference in a circuit when an electric current of 1 A is used. This relation is known as the Ohm’s Law.