Question

Question 4 (a)
How can three resistors of resistances $2\Omega ,3\Omega$ and $6\Omega$ be connected to give a total resistance of
(a) $4\Omega$?

Answer 1

There are three resistors of resistances $2\Omega ,3\Omega$, and $6\Omega$ respectively.
(a) The following circuit diagram shows the connection of the three resistors (By trial and error method).

Here, $6\Omega$ and $3\Omega$ resistors are connected in parallel.
Therefore, their equivalent resistance will be given by,
$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$
$\frac{1}{R}=\frac{1}{6}+\frac{1}{3}=\frac{6+3}{6\times 3}$
$R=2\Omega$
This equivalent resistor of resistance $2\Omega$ is connected to a $2\Omega$ resistor in series.
Therefore, the equivalent resistance of the circuit is given by,
$R=R_1+R_2$
$=2\Omega +2\Omega =4\Omega$
Hence, the equivalent resistance of the circuit is $4\Omega$.