Given:
• R1 = 3 Ω
,• R2 = 4 Ω
,• R3 = 4 Ω
,• R4 = 1 Ω
Let's find the equivalent resistance between A and B in the given circuit.
R3 and R4 are connected in parallel.
To find the equivalent resistance (R5) of R3 and R4 since they are connected in parallel, we have:
[tex]\begin{gathered} \frac{1}{R_5}=\frac{1}{R_3}+\frac{1}{R_4} \\ \\ \frac{1}{R_5}=\frac{1}{4}+\frac{1}{1} \\ \\ \frac{1}{R_5}=\frac{1+4}{4} \\ \\ \frac{1}{R_5}=\frac{5}{4} \\ \\ R_5=\frac{4}{5}=0.8\text{ \Omega} \end{gathered}[/tex]Now, R1, R2, and R5 are will be series.
To find the equivalent resistance, we have:
[tex]\begin{gathered} R_{eq}=R_1+R_2+R_3 \\ \\ R_{eq}=3Ω+4Ω+0.8Ω \\ \\ R_{eq}=7.8Ω \end{gathered}[/tex]Therefore, the equivalent resistance between A and B in the figure is 7.8Ω.
ANSWER:
7.8Ω