Question

What is the minimum resistance which can be made using five resistors each of $\frac{1}{5}\Omega$ .

• A. $\frac{1}{5}\Omega$
• B. $\frac{1}{25}\Omega$
• C. $\frac{1}{10}\Omega$
• D. $25\Omega$

Answer 1

The correct option is B

$\frac{1}{25}\Omega$

Step1: Given data

Every five resistors are of $\frac{1}{5}\Omega$

Step2: Resistors in parallel

1. When the voltage across the resistors is the same, the circuit is said to be linked in parallel.
2. In a parallel circuit, a resistor or any other component can be readily attached or detached without impacting the other elements.
3. The current in a series connection is constant, whereas the voltage in a parallel connection is constant throughout the circuit.
4. As a result, parallel connections are favored in household equipment.
5. Demonstrating with the help of a figure

Step3: The formula for parallel resistors

$\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+....+\frac{1}{R_n}[where{R}_1,R_2,....,R_{n}aretheresistorsconnectedinparallel.]$

Step4: Calculating the minimum resistance

Connecting the resistors in parallel

$$\begin{gathered} \frac{1}{R}=\frac{1}{{\displaystyle \frac{1}{5}}}+\frac{1}{{\displaystyle \frac{1}{5}}}+\frac{1}{{\displaystyle \frac{1}{5}}}+\frac{1}{{\displaystyle \frac{1}{5}}}+\frac{1}{{\displaystyle \frac{1}{5}}} \\ \frac{1}{R}=5+5+5+5+5 \\ \frac{1}{R}=25\Omega \\ R=\frac{1}{25}\Omega \end{gathered}$$

Hence, The minimum resistance is obtained when resistors are connected in parallel.