The resistance of the given circuit is 12 Ω.
What is resistance?
Resistance is given as the force that decelerates the current flow in the circuit. The resistance can be given in series and parallel connections.
In the given circuit diagram, R2 and R3 are in parallel connections. The resistance of R2 and R3 (R') is given as:
[tex]\rm \dfrac{1}{R'}=\dfrac{1}{R2}\;+\;\dfrac{1}{R3}\\\\ \dfrac{1}{R'}=\dfrac{1}{2}\;+\;\dfrac{1}{6}\\\\\dfrac{1}{R'}= \dfrac{1}{8} \\\\R'=8[/tex]
The R1 resistance is in series with R2 and R3, thus, the total resistance (R) can be given with:
R = R1 + R'
R = 4 + 8
R = 12
Thus, the resistance of the given circuit is 12 Ω.
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