Question

How will you connect three resistors of resistance $2\Omega$, $3\Omega$ and $6\Omega$ to obtain a total resistance of : (a) $4\Omega$ and (b) $1\Omega$?

Answer 1

There are three resistors of resistances 2 $\Omega$, 3 $\Omega$, and 6 $\Omega$ respectively.

(a) If we connect the given three resistors in the following way then we get net resistance as 4 $\Omega$.

$R_{eq}=\left(6||3\right)+2=\frac{6\times 3}{6+3}+2=2+2=4\Omega$

(b) If we connect the given three resistors in the following way then we get net resistance as 1 $\Omega$. Here all the resistors are connected in parallel

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

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