Question

How can three resistors of resistances $2\Omega ,3\Omega$ and $6\Omega$ be connected to give a total resistance of $1\Omega$?

Answer 1

Step 1: Given Data

The given resistances are,

$R_1=2\Omega ;R_2=3\Omega$ and $R_3=6\Omega$

As the value of the equivalent resistance is less than the resistance of each resistor thus, the resistors $R_1,R_2$ and $R_3$ must be connected in parallel.

Step 2: Formula used

Therefore, their equivalent resistance,

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

Step 3: Calculate the equivalent resistance

$\frac{1}{R_{eq}}=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$

$=\frac{3+2+1}{6}$

$=\frac{6}{6}$

$=1$

$\therefore R_{eq}=1\Omega$

Hence, the resistors $2\Omega ,3\Omega$ and $6\Omega$ kept in parallel to give a total resistance of $1\Omega$.