Question

Determine the equivalent resistance between A and B in the figure below.

Answer 1

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:

$\begin{gathered} \frac{1}{R_5}=\frac{1}{R_3}+\frac{1}{R_4} \\ \\ \frac{1}{R_5}=\frac{1}{4}+\frac{1}{1} \\ \\ \frac{1}{R_5}=\frac{1+4}{4} \\ \\ \frac{1}{R_5}=\frac{5}{4} \\ \\ R_5=\frac{4}{5}=0.8\text{ \Omega} \end{gathered}$

Now, R1, R2, and R5 are will be series.

To find the equivalent resistance, we have:

$\begin{gathered} R_{eq}=R_1+R_2+R_3 \\ \\ R_{eq}=3Ω+4Ω+0.8Ω \\ \\ R_{eq}=7.8Ω \end{gathered}$

Therefore, the equivalent resistance between A and B in the figure is 7.8Ω.

ANSWER:

7.8Ω