A triangle-shaped arrangement of three $3\Omega$ Resistances is used. Between any two corners, there will be a total of:

Resistance: The hindrance placed in the way of the current's flow is referred to as resistance. R stands for it.

Resistances in series are two or more resistances connected one after another such that the same current passes through them.

In a series combination, the comparable resistance is going to be ${\mathrm{R}}_{\mathrm{ser}}={\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{R}}_3$

Resistances are referred to as being in parallel when their terminals are connected at the same two places and there is an equal potential difference between them.

The formula for the net resistance/equivalent resistance (R) of parallel resistances is:

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$

It is given that, three $3\Omega$ resistors are connected to form a triangle. So, from the above figure, it is clear that resistors $R_{AB}$ and $R_{AC}$ are in series. Therefore, their equivalent resistance will be-

$\Rightarrow R_{\mathrm{ser}}=R_{AB}+R_{BC}$

$\Rightarrow R_{\text{ser }}=3\Omega +3\Omega =9\Omega$

Now resistors $R_{ser}$ and $R_{BC}$ are in parallel with each other. Therefore, their equivalent resistance will be

$\Rightarrow \frac{1}{R_{\text{para }}}=\frac{1}{R_{B}C}+\frac{1}{R_{\text{ser }}}$

$\Rightarrow \frac{1}{R_{\text{para }}}=\frac{1}{3}+\frac{1}{4}=\frac{7}{12}$

$\Rightarrow R_{\mathrm{para}}=\frac{12}{7}\Omega$.